Nihonkai Mathematical Journal Articles (Project Euclid)

Words from the Editors

Thu, 05 Aug 2010 15:41 EDT

Source: Nihonkai Math. J., Volume 20, Number 1.

Geometric realizations of curvature

Thu, 05 Aug 2010 15:41 EDT

Miguel Brozos-Vázquez, Peter Gilkey, Stana Nikčević

Source: Nihonkai Math. J., Volume 20, Number 1, 1--24.

Abstract:
We study geometric realization questions of curvature in the affine, Riemannian, almost Hermitian, almost para Hermitian, almost hyper Hermitian, almost hyper para Hermitian, Hermitian, and para Hermitian settings. We also express questions in Ivanov-Petrova geometry, Osserman geometry, and curvature homogeneity in terms of geometric realizations.

Remarks on some almost Hermitian structure on the tangent bundle

Thu, 05 Aug 2010 15:41 EDT

Takuya Koike, Takashi Oguro, Norio Watanabe

Source: Nihonkai Math. J., Volume 20, Number 1, 25--32.

Abstract:
In [5], M. Tahara and Y. Watanabe constructed a family of almost Hermitian structures ( J , G ) on the tangent bundle TM of a Riemannian manifold and constructed a family of Hermitian and Kähler structure on the tangent bundle on a space form. It is well-known that there are sixteen classes of almost Hermitian manifolds ([3]). In this paper, we give the conditions for ( J , G ) such that TM belongs to each of these sixteen classes.

On generalized Mannheim curves in Euclidean 4-space

Thu, 05 Aug 2010 15:41 EDT

Hiroo Matsuda, Shinsuke Yorozu

Source: Nihonkai Math. J., Volume 20, Number 1, 33--56.

Abstract:
We give a definition of generalized Mannheim curve in Euclidean 4-space E 4 . We show some characterizations and examples of generalized Mannheim curves.

Weighted composition operators on the logarithmic Bloch spaces with iterated weights

Thu, 05 Aug 2010 15:41 EDT

Takuya Hosokawa, Nguyen Quang Dieu

Source: Nihonkai Math. J., Volume 20, Number 1, 57--72.

Abstract:
We will characterize the boundedness and compactness of weighted composition operators on the logarithmic Bloch spaces with iterated weights on the open unit disk.

A ternary characterization of automorphisms of ${\mathbb B}({\mathscr H})$

Fri, 08 Apr 2011 09:10 EDT

Ali Taghavi Jelodar, Mohammad Sal Moslehian, Abolfazl Sanami

Source: Nihonkai Math. J., Volume 21, Number 1, 1--9.

Abstract:
If ${\mathscr H}$ is a Hilbert space, $\varphi$ is a (not necessary linear) $*$-surjective mapping on ${\mathbb B}({\mathscr H})$ and $\varphi$ preserves the spectrum of operators of the form $ABA^{*}$, then $\varphi$ is either an algebra automorphism or an algebra anti-automorphism.

Dunkl-Williams inequality for operators associated with $p$-angular distance

Fri, 08 Apr 2011 09:10 EDT

Farzad Dadipour, Masatoshi Fujii, {Mohammad Sal Moslehian

Source: Nihonkai Math. J., Volume 21, Number 1, 11--20.

Abstract:
We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-angular distance for operators. More precisely, we show that if $A, B \in \mathbb{B}(\mathscr{H})$ such that $|A|$ and $|B|$ are invertible, $\frac{1}{r}+\frac{1}{s}=1$ $(r>1)$ and $p\in\mathbb{R}$, then \begin{equation*} \left|\,A|A|^{p-1}-B|B|^{p-1}\,\right|^{2} \leq |A|^{p-1}\left(\,r|A-B|^{2}+s\left|\,|A|^{1-p}|B|^{p}-|B|\,\right|^2\,\right)|A|^{p-1}.%\nonumber \end{equation*} In the case that $0 < p \leq 1$, we remove the invertibility assumption and show that if $A=U|A|$ and $B=V|B|$ are the polar decompositions of $A$ and $B$, respectively, $t>0$, then $$\left|\,\left(U|A|^{p}-V|B|^{p}\right)|A|^{1-p}\,\right|^{2}\leq \left(1+t\strut\right)|A-B|^{2}+\left(1+\frac{1}{t}\right) \left| |B|^{p}|A|^{1-p}-|B| \right|^2 .$$ We obtain several equivalent conditions, when the case of equalities hold.

The stable rank and connected stable rank for certain non self-adjoint Banach algebras

Fri, 08 Apr 2011 09:10 EDT

Takahiro Sudo

Source: Nihonkai Math. J., Volume 21, Number 1, 21--34.

Abstract:
We consider the stable rank and connected stable rank for certain non self-adjoint Banach algebras such as the triangular matrix algebras of all (finite or infinite) triangular matrices over a unital Banach algebra and certain nest algebras. Also, the stable rank estimate for certain crossed products of unital Banach algebras by isometries is obtained.

Nonlinear scalarizations and some applications in vector optimization

Fri, 08 Apr 2011 09:10 EDT

Yousuke Araya

Source: Nihonkai Math. J., Volume 21, Number 1, 35--45.

Abstract:
We first give a little improvement of nonlinear scalarizing function for vector optimization problem organized by Luc and Tammer-Weidner. As applications, we present Gordan's type alternative theorems for vector-valued function, optimality conditions for vector optimization problem and an existence theorem for vector saddle-points.

Hypergroup extensions of finite Abelian groups by hypergroups of order two

Fri, 08 Apr 2011 09:10 EDT

Ryo Ichihara, Satoshi Kawakami, Masafumi Sakao

Source: Nihonkai Math. J., Volume 21, Number 1, 47--71.

Abstract:
The purpose of the present paper is to establish necessary conditions and sufficient conditions that finite commutative hypergroups are extensions of finite Abelian groups by hypergroups of order two. Applying our results to some concrete cases one can determine all such extensions.

Triple coverings of the projective plane branched along quintic curves

Fri, 22 Apr 2011 09:08 EDT

Tadasuke Yasumura

Source: Nihonkai Math. J., Volume 21, Number 2, 73--89.

Abstract:
In this article, we characterize triple coverings over the projective plane $\mathbb{P}^{2}$ branched along quintic curves with some conditions. The main result is that such triple coverings are induced by projections $\mathbb{P}^{3} \dasharrow \mathbb{P}^{2}$ from certain points.

Cone-semicontinuity of set-valued maps by analogy with real-valued semicontinuity

Fri, 22 Apr 2011 09:08 EDT

Yuuya Sonda, Issei Kuwano, Tamaki Tanaka

Source: Nihonkai Math. J., Volume 21, Number 2, 91--103.

Abstract:
In the paper, we propose how we can treat several kinds of semicontinuity with respect to cone for set-valued maps by analogy with semicontinuity for real-valued functions and investigate the inheritance properties on cone-(semi)continuity of parent set-valued maps via scalarization.

A generalization of the Banach-Stone theorem for commutative Banach algebras

Fri, 22 Apr 2011 09:08 EDT

Go Hirasawa, Takeshi Miura, Rumi Shindo

Source: Nihonkai Math. J., Volume 21, Number 2, 105--114.

Abstract:
Let $I$ be an index set, not necessarily a subset of any Banach algebra. Let $\mathcal{A}$ and $\mathcal{B}$ be unital semisimple commutative Banach algebras with maximal ideal spaces $M_{\mathcal{A}}$ and $M_{\mathcal{B}}$, respectively. If surjective mappings $S_1, S_2 \colon I \to \mathcal{A}$ and $T_1, T_2 \colon I \to \mathcal{B}$ satisfy $\mathrm{r}(T_1(\lambda) - T_2(\mu)) = \mathrm{r}(S_1(\lambda) - S_2(\mu))$ for all $\lambda, \mu \in I$, where $\mathrm{r}(a)$ is the spectral radius of $a$, then there exist $p, w \in \mathcal{B}$, a homeomorphism $\varphi \colon M_\mathcal{B} \to M_\mathcal{A}$ and a closed and open subset $K$ of $M_\mathcal{B}$ such that $|\hat{w}| = 1$ on $M_\mathcal{B}$ and that $$ \widehat{T_k(\lambda)}(y) - \hat{p}(y) = \begin{cases} \hat{w}(y)\widehat{S_k(\lambda)}(\varphi(y)) & y \in K \\[2pt] \hat{w}(y)\overline{\widehat{S_k(\lambda)}(\varphi(y))} & y \in M_\mathcal{B} \setminus K \end{cases} $$ for all $\lambda \in I$ $(k = 1, 2)$. In particular, if $\mathcal{A}$ and $\mathcal{B}$ are uniform algebras, and if $S_1, S_2 \colon I \to \mathcal{A}$ and $T_1, T_2 \colon I \to \mathcal{B}$ satisfy $$ \sigma_\pi ({T_1(\lambda) - T_2(\mu)}) \cap \sigma_pi ({S_1(\lambda) - S_2(\mu)} ) \neq \emptyset \qquad (\forall \lambda, \mu \in I), $$ where $\sigma_pi (f)$ is the peripheral spectrum of $f$, then $\widehat{T_k(\lambda)}(y) = \hat{p}(y) + \widehat{S_k(\lambda)}(\varphi(y))$ for all $\lambda \in I$ and $y \in M_\mathcal{B}$ $(k = 1, 2)$.

A polynomially spectrum preserving map between uniform algebras

Fri, 22 Apr 2011 09:08 EDT

Go Hirasawa, Hirokazu Oka

Source: Nihonkai Math. J., Volume 21, Number 2, 115--119.

Abstract:
We determine the general forms of polynomially spectrum preserving maps between uniform algebras for polynomials of the type $p(z,w)=zw+az+bw+c$.

On Some Types of Vectoral Saddle-point Problems

Thu, 14 Jun 2012 13:14 EDT

Kenji Kimura

Source: Nihonkai Math. J., Volume 22, Number 1, 1--21.

Abstract:
In the paper, we consider some types of vectorial saddle-point problems. We present some existence results of vectorial saddle-point problems. After that we consider a generalized vector equilibrium problem as an application.

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Thu, 14 Jun 2012 13:14 EDT

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Source: Nihonkai Math. J., Volume 22, Number 1, 23--37.

Abstract:
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Garden Representation and Interior Variation of Real Rational Functions

Thu, 14 Jun 2012 13:14 EDT

Sayaka Tamae

Source: Nihonkai Math. J., Volume 22, Number 1, 39--47.

Abstract:
In this paper, we show that the fundamental surgeries of the graph representation for real rational functions can be achieved by classical interior variations essentially due to Schiffer. As an application we give a constructive proof of the main theorem of Natanzon, Shapiro and Vainshtein in [2].

Notes on Vertex Atlas of Danzer Tiling

Thu, 14 Jun 2012 13:14 EDT

Hiroko Hayashi, Yuu Kawachi, Kazushi Komatsu, Aya Konda, Miho Kurozoe, Fumihiko Nakano, Naomi Odawara, Rika Onda, Akinobu Sugio, Masatetsu Yamauchi

Source: Nihonkai Math. J., Volume 22, Number 1, 49--58.

Abstract:
In this note, we study in detail the remark in the appendix of Danzer [6]. We find that planer Danzer tilings have many different aspects than Penroze tilings. For e.g., we observe that Danzer tiling with 7-fold symmetry does not belong to the topological closure of tilings generated by up-down generation.

The Subdivision of the Window Derived from Finite Subsequences of Fibonacci Sequences

Thu, 14 Jun 2012 13:58 EDT

Hiroko Hayashi

Source: Nihonkai Math. J., Volume 22, Number 2, 59--66.

Abstract:
The Fibonacci sequences can be identified with 1-dimensional quasiperiodic tilings by the canonical projection method. We divide the window of the canonical projection method into smaller intervals by using local configurations. Then, we show that the intervals which appears in the window are divided into the ratio at $1:1/\tau:1$ ad infinitum.

On the Category of Confinite Modules for Principal Ideals

Thu, 14 Jun 2012 13:58 EDT

Ken-Ichiroh Kawasaki

Source: Nihonkai Math. J., Volume 22, Number 2, 67--71.

Abstract:
In this paper, it is pointed out that ${\mathcal M}(A, I)_{cof}$ is an Abelian full subcategory of the category ${\mathcal M}(A)$ consisting of all $A$-modules for a principal ideal $I$ over a noetherian ring $A$.

Linear Isometries on Spaces of Continulously Differentiable and Lipschitz Continuous Functions

Thu, 14 Jun 2012 13:58 EDT

Hironao Koshimizue

Source: Nihonkai Math. J., Volume 22, Number 2, 39--47.

Abstract:
We characterize the surjective linear isometries on $C^{(n)} [0, 1]$ and Lip$[0, 1]$. Here $C^{(n)} [0, 1]$ denotes the Banach space of $n$-times continuously differentiable functions on $[0, 1]$ equipped with the norm \begin{equation*} \| f \| = \sum_{k=0}^{n-1}|f^{(k)} (0)| + \sup _{x \in [0, 1]} | f^{(n)} (x) | \quad (f \in C^{(n)} [0, 1]) , \end{equation*} and Lip$[0, 1]$ denotes the Banach space of Lipschitz continuous functions on $[0, 1]$ equipped with the norm \begin{equation*} \| f \| = |f(0)| + \mathop{\operatorname{ess \, sup}} _{x \in [0, 1]} | f' (x) | \quad (f \in {\rm Lip}[0, 1]). \end{equation*}

The Monotonicity of Absolute Normalized Norms on $\mathbb{C}^n$

Thu, 14 Jun 2012 13:58 EDT

Ken-Ichi Mitani, Kichi-Suke Saito, Naoto Komuro

Source: Nihonkai Math. J., Volume 22, Number 2, 91--102.

Abstract:
In this paper, we characterize some monotonicity property of absolute normalized norms on $\mathbb{C}^n$ (resp. $\mathbb{R}^n$) by means of their corresponding continuous convex functions.

Properties on C*-algebras with or without residual dimension finite

Mon, 05 Nov 2012 09:11 EST

Takahiro Sudo

Source: Nihonkai Math. J., Volume 23, Number 1, 1--10.

Abstract:
We study and develope a general theory for C*-algebras by considering their residual dimension. For this we introduce a renewed notion that is equivalent to RFD, to divide C*-algebras into two classes to be clarified as a main purpose.

On totally geodesic complex submanifords of pseudo-Bochner-flat locally conformal Kähler manifods in the Hermitian sense

Mon, 05 Nov 2012 09:11 EST

Koji Matsuo

Source: Nihonkai Math. J., Volume 23, Number 1, 11--19.

Abstract:
We prove the l.c.K. version of the characterization theorem, due to B.-Y. Chen, L. Vanhecke and L. Verstraelen, for totally geodesic complex submanifolds of Bochner-flat Kähler manifolds. 1.

Quasiasymptotics in exponential distributions by wavelet analysis

Mon, 05 Nov 2012 09:11 EST

Byung Keun Sohn

Source: Nihonkai Math. J., Volume 23, Number 1, 39--47.

Abstract:
We investigate the quasiasymptotics of exponential distributions at a point or infinity via its multiresolution expansion. We also analyse the boundedness of the wavelet transform and wavelet coefficients of quasiasymptotically bounded exponential distributions.

The asymptotic behavior of geodesic crcles in 2-torus of revolution and a sub-ergodic property

Mon, 05 Nov 2012 09:11 EST

Nobuhiro Innami

Source: Nihonkai Math. J., Volume 23, Number 1, 43--55.

Abstract:
Let $M$ be a complete Riemannian manifold with finite volume and $G_t$ the geodesic flow on the unit tangent bundle $SM$. In the light of the Poincaré recurrence property we study the following properties. (P1) For any point $p \in M$ and any open set $ U \subset M $ there exists an $R > 0$ such that $\pi(G_t(S_pM)) \cap U \neq \emptyset$ for all $t > R$. (P2) For any unit tangent vector $x \in SM$ and any point $q \in M$ there exist a sequence of unit tangent vectors $x_n \in SM$ and a sequence $t_n \rightarrow \infty$ such that $x_n \rightarrow x$ and $\pi(G_{t_n}(x_n)) \rightarrow q$.

Errata to "Interpolation problem for $\ell^1$ and an $F$-space"

Mon, 05 Nov 2012 09:11 EST

Takahiko Nakazi

Source: Nihonkai Math. J., Volume 23, Number 1, 43--55.

An example of $2\times 2$ hyperbolic conservation laws admitting delta-shock waves

Tue, 12 Mar 2013 09:50 EDT

Hiroki Ohwa

Source: Nihonkai Math. J., Volume 23, Number 2, 59--75.

Abstract:
In this paper we show that for some specific initial data, the Riemann problem for a simple model of $2\times 2$ hyperbolic conservation laws has solutions containing delta-shock waves.

Characterization and automatic continuity of separating maps between Banach modules

Tue, 12 Mar 2013 09:50 EDT

Lida Mousavi, Fereshteh Sady

Source: Nihonkai Math. J., Volume 23, Number 2, 75--91.

Abstract:
A linear map $T:\mathcal{A}\to \mathcal{B}$ between algebras (or spaces of functions) $\mathcal{A}$ and $\mathcal{B}$ is called separating if $x \cdot y=0$ implies $Tx\cdot Ty=0$ for all $x,y\in \mathcal{A}$. It is well known that a separating map between certain commutative semisimple Banach algebras is very close to being a weighted composition operator on the maximal ideal spaces. In this paper, after introducing the notion of the cozero set for the elements of a Banach module, we first extend the notion of the separating maps to Banach module case. Our approach depends on the notion of point multipliers on a Banach module $\mathcal{X}$ and the relation between hyper maximal submodules of $\mathcal{X}$ and point multipliers on it. Then we generalize some well known results about separating maps between certain subspaces of continuous functions to Banach module case. In particular, we show that, imposing some additional assumptions on Banach modules, such map can be represented as a variation of a weighted composition operator. We also obtain a result concerning the automatic continuity of a bijective separating map whose inverse is also separating.

The Dunkl-Williams constant of symmetric octagonal norms on $\mathbb{R}^2$

Tue, 12 Mar 2013 09:50 EDT

Hiroyasu Mizuguchi, Kichi-Suke Saito, Ryotaro Tanaka

Source: Nihonkai Math. J., Volume 23, Number 2, 93--113.

Abstract:
Recently, we constructed a new calculation method for the Dunkl-Williams constant $DW(X)$ of a normed linear space $X$. In this paper, we determine the Dunkl-Williams constant of symmetric octagonal norms on $\mathbb{R}^2$ by using our method.

Approximation of Common Solutions for Monotone Inclusion Problems and Equilibrium Problems in Hilbert Spaces

Tue, 12 Mar 2013 09:50 EDT

Mayumi Hojo, Wataru Takahashi

Source: Nihonkai Math. J., Volume 23, Number 2, 115--134.

Abstract:
Let $H$ be a real Hilbert space and let $C$ be a nonempty closed convex subset of $H$. Let $\alpha >0$ and let $A$ be an $\alpha$-inverse-strongly monotone mapping of $C$ into $H$. Let $B$ be a maximal monotone operator on $H$ and let $F$ be a maximal monotone operator on $H$ such that the domain of $F$ is included in $C$. Let $(A+B)^{-1}0$ and $F^{-1}0$ be the sets of zero points of $A+B$ and $F$, respectively. Let $0< k<1$ and let $g$ be a $k$-contraction of $H$ into itself. Let $G$ be a strongly positive bounded linear self-adjoint operator on $H$ with coefficient $\overline{\gamma}>0$ and let $0< \gamma <\frac{\overline{\gamma}}{k}$. In this paper, under the assumption $(A+B)^{-1}0 \cap F^{-1}0 \neq \emptyset$, In this paper, we prove a strong convergence theorem for finding a point $z_0\in (A+B)^{-1}0\cap F^{-1}0$ which is a unique fixed point of a nonlinear operator and also a unique solution of a variational inequality. $z_0\in (A+B)^{-1}0\cap F^{-1}0$ is a unique fixed point of $P_{(A+B)^{-1}0\cap F^{-1}0}(I-G+\gamma g)$. This point $z_0\in (A+B)^{-1}0\cap F^{-1}0$ is also a unique solution of a variational inequality. Using this result, we obtain new and well-known strong convergence theorems in a Hilbert space which are useful in Nonlinear Analysis and Optimization.