Rocky Mountain Journal of Mathematics

A note on skew product preserving maps on factor von Neumann algebras

Ali Taghavi and Hamid Rohi

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Let $\mathcal {A}$ be a factor von Neumann algebra, with unit $ I $, which contains a nontrivial projection $ P_{1} $, and let $\psi :\mathcal {A} \rightarrow \mathcal {A}$ be a surjective map that satisfies one of the two conditions: $\psi (A)\psi (P) + \lambda \psi (P)\psi (A) = AP + \lambda PA$ and $\psi (A)\psi (P) + \lambda \psi (P)\psi (A)^{\ast } = AP + \lambda PA^{\ast }$ for all $A \in \mathcal {A}$ and $P \in \lbrace P_{1}, I - P_{1}\rbrace $ and $\lambda \in \lbrace -1, 1\rbrace $. Then, we determine the concrete form of $\psi $.

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Rocky Mountain J. Math., Volume 47, Number 6 (2017), 2083-2094.

First available in Project Euclid: 21 November 2017

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Zentralblatt MATH identifier

Primary: 47B48: Operators on Banach algebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]

Preserving problems skew products von Neumann algebras


Taghavi, Ali; Rohi, Hamid. A note on skew product preserving maps on factor von Neumann algebras. Rocky Mountain J. Math. 47 (2017), no. 6, 2083--2094. doi:10.1216/RMJ-2017-47-6-2083.

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  • M. Brešar and M. Fsoňer, On rings with involution equipped with some new product, Publ. Math. Debrecen 57 (2000), 121–134.
  • M.A. Chebotar, Y. Fong and P.-H. Lee, On maps preserving zeros of the polynomial $ xy - yx^{\ast} $, Linear Alg. Appl. 408 (2005), 230–243.
  • J. Cui and J. Hou, Linear maps preserving elements annihilated by a polynomial $XY-YX^{\dagger}$, Stud. Math. 174 (2006), 183–199.
  • J. Cui and C. Park, Maps preserving strong skew Lie product on factor von Neumann algebras, Acta Math. Sci. 32 (2012), 531–538.
  • L. Molnar, A condition for a subspace of $B(H)$ to be an ideal, Linear Alg. Appl. 235 (1996), 229–234.
  • X. Qi and J. Hou, Strong skew commutativity preserving maps on von Neumann algebras, Math. Anal. Appl. 397 (2013), 362–370.
  • P. Šemrl, On Jordan $^{\ast}$-derivations and an application, Colloq. Math. 59 (1990), 241–251.
  • ––––, Quadratic functionals and Jordan $^{\ast}$-derivations, Stud. Math. 97 (1990), 157–165.
  • A. Taghavi, V. Darvish and H. Rohi, Additivity of maps preserving products $ AP \pm PA^{\ast}$ on $ C^{\ast}$-algebras, Math. Slov. 67 (2017), 213–220.
  • A. Taghavi, H. Rohi and V. Darvish, Additivity of maps preserving Jordan $\eta_{\ast}$-products on $C^{*}$-algebras, Bull. Iranian Math. Soc. 41 (2015), 107–116.
  • ––––, Nonlinear $^{\ast}$-Jordan derivations on von Neumann algebras, Lin. Multilin. Alg. 64 (2016), 426–439.