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- W3021143862 abstract "Let X be a complex Banach space and denote by B ( X ) the algebra of all linear bounded operators on X . For T ∈ B ( X ) , denote by r ( T ) its spectral radius. We prove that if φ : B ( X ) → B ( X ) is a linear and surjective map such that i) given any A , B ∈ B ( X ) , there exists a positive real number M A , B such that r ( φ ( A ) + λ φ ( B ) ) ≤ M A , B r ( A + λ B ) for all complex numbers λ satisfying | λ | ≤ 1 ; ii) r ( φ ( T ) ) = 0 implies r ( T ) = 0 , then there exist a linear functional f : B ( X ) → C , a nonzero complex number c and either a bounded invertible linear map U : X → X such that φ ( T ) = c U T U − 1 + f ( T ) I ( T ∈ B ( X ) ) , or a bounded invertible linear map U : X ⁎ → X such that φ ( T ) = c U T ⁎ U − 1 + f ( T ) I ( T ∈ B ( X ) ) . Also, the linear functional f satisfies the property that given any A , B ∈ B ( X ) there exists N A , B ≥ 0 such that | f ( A ) + λ f ( B ) | ≤ N A , B r ( A + λ B ) for all complex numbers λ satisfying | λ | ≤ 1 ." @default.
- W3021143862 created "2020-05-13" @default.
- W3021143862 creator A5013275456 @default.
- W3021143862 date "2020-10-01" @default.
- W3021143862 modified "2023-09-27" @default.
- W3021143862 title "On spectrally bounded linear maps on B(X)" @default.
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- W3021143862 doi "https://doi.org/10.1016/j.jmaa.2020.124206" @default.
- W3021143862 hasPublicationYear "2020" @default.
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