Linear maps preserving the dimension of fixed points of operators

2013/09/13 by Ali Taghavi, Taghavi, Ali, Roja Hosseinzadeh +1
Computer Science · Mathematics · #46J10 #47B48 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1309.3429

openalex publication_date 2013/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Maps preserving the fixed points of products of operators
• Comment on Maps preserving the dimension of fixed points of products of operators
• Maps preserving the idempotency of Jordan products
• Additive maps preserving the reduced minimum modulus of Banach space operators
• Maps completely preserving involution