Maps preserving the square zero of ?-Lie product of operators

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-03-0036

Keywords:

Preserver problem, Square zero operator, η-Lie product

Abstract

Let B(H) be the algebra of all bounded linear operators on an infinite dimensional Hilbert space ?. In this paper, we identify the form of the unital surjective additive map ? : B(H)? B(H)which preserves the square zero of ?-Lie product of operators for some scalar ? with ? ? 0, 1, ?1.

Author Biographies

Ali Taghavi, University of Mazandaran.

Dept. of Mathematics.

Roja Hosseinzadeh, University of Mazandaran.

Dept. of Mathematics.

Masoomeh Yousefi, University of Mazandaran.

Dept. of Mathematics.

References

M. A. Chebotar, W.-F. Ke, P.-H. Lee, and N.-C. Wong, “Mappings preserving zero products”, Studia mathematica, vol. 155, no. 1, pp. 77–94, 2003, doi: 10.4064/sm155-1-6

M. Dobovišek, B. Kuzma, G. Lešnjak, C. Li, and T. Petek, “Mappings that preserve pairs of operators with zero triple Jordan product”, Linear algebra and its applications, vol. 426, no. 2-3, pp. 255–279, Oct. 2007, doi: 10.1016/j.laa.2007.04.017

G. Dolinar, S. Du, J. Hou, and P. Legiša, “General preservers of invariant subspace lattices”, Linear algebra and its applications, vol. 429, no. 1, pp. 100–109, Jul. 2008, doi: 10.1016/j.laa.2008.02.007

L. Fang, G. Ji, and Y. Pang, “Maps preserving the idempotency of products of operators”, Linear algebra and its applications, vol. 426, no. 1, pp. 40–52, Oct. 2007, doi: 10.1016/j.laa.2007.03.030

J. Hou and L. Huang, “Maps completely preserving idempotents and maps completely preserving square-zero operators”, Israel journal of mathematics, vol. 176, no. 1, pp. 363–380, Mar. 2010, doi: 10.1007/s11856-010-0032-y

L. Molnár, “Non-linear Jordan triple automorphisms of sets of self-adjoint matrices and operators”, Studia mathematica, vol. 173, no. 1, pp. 39–48, 2006, doi: 10.4064/sm173-1-3

P. Šemrl, “Linear mappings that preserve operators annihilated by a polynomial”, Journal of operator theory, 36, pp. 45-58, 1996. [On line]. Available: https://bit.ly/2ZCJnB1

A. Taghavi and R. Hosseinzadeh, “Maps preserving the dimension of fixed points of products of operators”, Linear and multilinear algebra, vol. 62, no. 10, pp. 1285–1292, Sep. 2013, doi: 10.1080/03081087.2013.823680

A. Taghavi, R. Hosseinzadeh, and H. Rohi, “Maps preserving the fixed points of sum of operators”, Operators and matrices, no. 3, pp. 563–569, 2015, doi: 10.7153/oam-09-34

A. Taghavi, F. Kolivand, and H. Rohi, “A note on strong η-Lie products preserving maps on some algebras”, Mediterranean journal of mathematics, vol. 14, no. 1, 2017, doi: 10.1007/s00009-016-0824-3

M. Wang, L. Fang, and G. Ji, “Linear maps preserving idempotency of products or triple jordan products of operators”, Linear algebra and its applications, vol. 429, no. 1, pp. 181–189, Jul. 2008, doi: 10.1016/j.laa.2008.02.013

J.-H. Zhang and F.-J. Zhang, “Nonlinear maps preserving Lie products on factor von Neumann algebras”, Linear algebra and its applications, vol. 429, no. 1, pp. 18–30, Jul. 2008, doi: 10.1016/j.laa.2008.01.031

Published

2020-06-03

How to Cite

[1]
A. Taghavi, R. Hosseinzadeh, and M. Yousefi, “Maps preserving the square zero of ?-Lie product of operators”, Proyecciones (Antofagasta, On line), vol. 39, no. 3, pp. 591-597, Jun. 2020.

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Artículos