A generalization of peripherally-multiplicative surjections between standard operator algebras

• Autorzy: Takeshi Miura , Dai Honma
• Języki publikacji: EN

Abstrakty

EN

Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B −1 for some bijective bounded linear operators B 1;B 2 of X* onto Y.

Słowa kluczowe

EN

Standard operator algebra; Peripheral spectrum; Peripherally-multiplicative operator; Spectrum-preserving map

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 47L10: Algebras of operators on Banach spaces and other topological linear spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 3
• Strony: 479-486

Daty

wydano

2009-09-01

online

2009-08-12

Twórcy

autor

Takeshi Miura

• Yamagata University

autor

Dai Honma

• Uchida Unicom Co., Ltd.

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0033-4