Maps Preserving the Spectrum of Skew Lie Product of Operators


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Authors: E. ALZEDANI AND M. MABROUK

DOI: 10.46793/KgJMat2204.525A

Abstract:



Keywords:

Nonlinear preservers, spectrum, Skew Lie product.



References:

[1]   Z. Abdelali, Maps preserving the spectrum of polynomial products of matrices, J. Math. Anal. Appl. 480 (2019), Paper ID 123392.

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[4]   A. Bourhim and J. Mashreghi, Maps preserving the local spectrum of triple product of operators, Linear Multilinear Algebra (2014), 1–9.

[5]   A. Bourhim and J. Mashreghi, Maps preserving the local spectrum of product of operators, Glasg. Math. J. 57 (2015), 709–718.

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[7]   A. Bourhim, J. Mashreghi and A. Stepanyan, Maps between Banach algebras preserving the spectrum, Arch. Math. 107 (2016), 609–621.

[8]   J.-T. Chan, C.-K. Li and N.-S. Sze, Mappings preserving spectra of products of matrices, Proc. Amer. Math. Soc. 135 (2007), 977–986.

[9]   C. Costara, Non-surjective spectral isometries on matrix spaces, Complex Anal. Oper. Theory 12 (2018), 859–868.

[10]   C. Costara and D. Repovš, Spectral isometries onto algebras having a separating family of finite-dimensional irreducible representations, J. Math. Anal. Appl. 365 (2010), 605–608.

[11]   J. Cui and P. Choonkil, Maps preserving strong skew Lie product on factor von Neumann algebras, Acta Math. Sci. 32 (2012), 531–538.

[12]   J.-L. Cui and C.-K. Li, Maps preserving peripheral spectrum of Jordan products of operators, Oper. Matrices 6 (2012), 129–146.

[13]    O. Hatori, T. Miura and H. Takagi, Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative, J. Math. Anal. Appl. 326 (2007), 281–296.

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Kragujevac Journal of Mathematics Vol. 46 No.4 (2022)