Linear maps preserving the dimension of fixed points of operators

TL;DR

This paper characterizes linear maps on operator algebras that preserve the dimension of the fixed point space, providing insights into their structure in finite-dimensional Banach spaces.

Contribution

It offers a new characterization of surjective linear maps preserving fixed point space dimensions in finite-dimensional Banach spaces.

Findings

Surjective linear maps preserving fixed point space dimension are characterized.

Linear maps preserving fixed point spaces are classified.

Results apply specifically to finite-dimensional Banach spaces.

Abstract

Let B(X) be the algebra of all bounded linear operators on a complex Banach space X with dim X greater than 3. In this paper, we characterize the forms of surjective linear maps on B(X) which preserve the dimension of the vector space containing of all fixed points of operators, whenever X is a fifinite dimensional Banach space. Moreover, we characterize the forms of linear maps on B(X) which preserve the vector space containing of all fixed points of operators.