Banach Journal of Mathematical Analysis

Generalized 3-circular projections for unitary congruence invariant norms

Abdullah Bin Abu Baker

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

A projection P0 on a complex Banach space is generalized 3- circular if its linear combination with two projections P1 and P2 having coefficients λ1 and λ2, respectively, is a surjective isometry, where λ1 and λ2 are distinct unit modulus complex numbers different from 1 and P0P1P2=I. Such projections are always contractive. In this paper, we prove structure theorems for generalized 3-circular projections acting on the spaces of all n×n symmetric and skew-symmetric matrices over C when these spaces are equipped with unitary congruence invariant norms.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 3 (2016), 451-465.

Dates
Received: 16 March 2015
Accepted: 17 August 2015
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1463153910

Digital Object Identifier
doi:10.1215/17358787-3599609

Mathematical Reviews number (MathSciNet)
MR3504179

Zentralblatt MATH identifier
1356.46010

Subjects
Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]

Keywords
spectral theorem isometry generalized 3-circular projection unitary congruence invariant norm

Citation

Abu Baker, Abdullah Bin. Generalized $3$ -circular projections for unitary congruence invariant norms. Banach J. Math. Anal. 10 (2016), no. 3, 451--465. doi:10.1215/17358787-3599609. https://projecteuclid.org/euclid.bjma/1463153910


Export citation

References

  • [1] A. B. Abubaker, F. Botelho, and J. Jamison, Representation of generalized bi-circular projections on Banach spaces, Acta Sci. Math. (Szeged) 80 (2014), nos. 3–4, 591–601.
  • [2] A. B. Abubaker and S. Dutta, Projections in the convex hull of three surjective isometries on $C(\Omega)$, J. Math. Anal. Appl. 379 (2011), no. 2, 878–888.
  • [3] A. B. Abubaker and S. Dutta, Structures of generalized $3$-circular projections for symmetric norms, Proc. Indian Acad. Sci. Math. Sci. published electronically 2 April 2016.
  • [4] S. J. Bernau and H. E. Lacey, Bicontractive projections and reordering of $L_{p}$-spaces, Pacific J. Math. 69 (1977), no. 2, 291–302.
  • [5] F. Botelho and J. Jamison, Generalized bi-circular projections on minimal ideals of operators, Proc. Amer. Math. Soc. 136 (2008), no. 4, 1397–1402.
  • [6] F. Botelho and J. Jamison, Generalized bi-circular projections on $C(\Omega,X)$, Rocky Mountain J. Math. 40 (2010), no. 1, 77–83.
  • [7] F. Botelho and J. Jamison, Algebraic reflexivity of sets of bounded operators on vector valued Lipschitz functions, Linear Algebra Appl. 432 (2010), no. 12, 3337–3342.
  • [8] S. Dutta and T. S. S. R. K. Rao, Algebraic reflexivity of some subsets of the isometry group, Linear Algebra Appl. 429 (2008), no. 7, 1522–1527.
  • [9] M. Fošner, D. Ilišević, and C. K. Li, $G$-invariant norms and bicircular projections, Linear Algebra Appl. 420 (2007), nos. 2–3, 596–608.
  • [10] R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge Univ. Press, Cambridge, 2013.
  • [11] D. Ilišević, Generalized bicircular projections on $JB^{*}$-triples, Linear Algebra Appl. 432 (2010), no. 5, 1267–1276.
  • [12] R. King, Generalized bi-circular projections on certain Hardy spaces, J. Math. Anal. Appl. 408 (2013), no. 1, 35–39.
  • [13] H. E. Lacey, The Isometric Theory of Classical Banach Spaces, Grundlehren Math. Wiss. 208, Springer, New York, 1974.
  • [14] C. K. Li, “Some aspects of the theory of norms” in Proceedings of the 3rd ILAS Conference (Pensacola, FL, 1993), Linear Algebra Appl. 212–213 (1994), 71–100.
  • [15] C. K. Li, Norms, isometries, and isometry Groups, Amer. Math. Monthly 107 (2000), no. 4, 334–340.
  • [16] A. Lima, Intersection properties of balls in spaces of compact operators, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, 35–65.
  • [17] P. K. Lin, Generalized bi-circular projections, J. Math. Anal. Appl. 340 (2008), no. 1, 1–4.
  • [18] J. Lindenstrauss, Extension of compact operators, Mem. Amer. Math. Soc. 112 (1964), no. 48.