Maps preserving fixed points of generalized product of operators

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-05-0071

Keywords:

Fixed point, Generalized product, Preserver problems

Abstract

Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. For A ? B(X) let F (A) be the subspace of fixed point of A. For an integer k ? 2, let (i1, .., im) be a finite sequence with terms chosen from {1, · · · , k}, and assume at least one of the terms in (i1, · · · , im) appears exactly once. The generalized product of k operators A1, ..., Ak ? B(X) is defined by A1 ? A2 ? · · · ? Ak = Ai? Ai? · · · Aim , and includes the usual product and the triple product. We characterize the form of maps from B(X) onto itself satisfying F (?(A1) ? · · · ? ?(Ak)) = F (A1 ? · · · ? Ak) for all A1, · · · , Ak ? B(X).

Author Biographies

Youssef Bouramdane, University Sidi Mohammed Ben Abdellah.

Dept. of Mathematics, LASMA Laboratory.

M. Ech-Cherif El Kettani, University Sidi Mohammed Ben Abdellah.

Dept. of Mathematics, LASMA Laboratory.

A. Elhiri, University Sidi Mohammed Ben Abdellah.

Dept. of Mathematics, LASMA Laboratory.

A. Lahssaini, University Sidi Mohammed Ben Abdellah.

Dept. of Mathematics, LASMA Laboratory.

References

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Published

2020-10-01

How to Cite

[1]
Y. Bouramdane, M. . Ech-Cherif El Kettani, A. Elhiri, and A. Lahssaini, “Maps preserving fixed points of generalized product of operators”, Proyecciones (Antofagasta, On line), vol. 39, no. 5, pp. 1157-1165, Oct. 2020.

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