Preservers of the local spectral radius zero of Jordan product of operators | Zendy

Mhamed Elhodaibi | Zendy; Somaya Saber | Zendy

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Preservers of the local spectral radius zero of Jordan product of operators

Author(s) -

Mhamed Elhodaibi,

Somaya Saber

Publication year - 2021

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.454

H-Index - 27

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-2010-88

Subject(s) - mathematics , spectral radius , surjective function , bounded function , zero (linguistics) , linear operators , banach algebra , product (mathematics) , radius , banach space , bounded operator , spectrum (functional analysis) , combinatorics , pure mathematics , mathematical analysis , geometry , physics , eigenvalues and eigenvectors , linguistics , philosophy , computer security , quantum mechanics , computer science

Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex Banach space X , and denote by rT (x) the local spectral radius of any operator T ∈ B(X) at any vector x ∈ X . In this paper, we characterize surjective maps φ on B(X) satisfying rφ(T )φ(A)+φ(A)φ(T )(x) = 0 if and only if rTA+AT (x) = 0 for all x ∈ X and A, T ∈ B(X) .

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