# A generalization of peripherally-multiplicative surjections between standard operator algebras

Open Mathematics (2009)

- Volume: 7, Issue: 3, page 479-486
- ISSN: 2391-5455

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topTakeshi Miura, and Dai Honma. "A generalization of peripherally-multiplicative surjections between standard operator algebras." Open Mathematics 7.3 (2009): 479-486. <http://eudml.org/doc/269375>.

@article{TakeshiMiura2009,

abstract = {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.},

author = {Takeshi Miura, Dai Honma},

journal = {Open Mathematics},

keywords = {Standard operator algebra; Peripheral spectrum; Peripherally-multiplicative operator; Spectrum-preserving map; standard operator algebra; peripheral spectrum; peripherally-multiplicative operator; spectrum-preserving map},

language = {eng},

number = {3},

pages = {479-486},

title = {A generalization of peripherally-multiplicative surjections between standard operator algebras},

url = {http://eudml.org/doc/269375},

volume = {7},

year = {2009},

}

TY - JOUR

AU - Takeshi Miura

AU - Dai Honma

TI - A generalization of peripherally-multiplicative surjections between standard operator algebras

JO - Open Mathematics

PY - 2009

VL - 7

IS - 3

SP - 479

EP - 486

AB - 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.

LA - eng

KW - Standard operator algebra; Peripheral spectrum; Peripherally-multiplicative operator; Spectrum-preserving map; standard operator algebra; peripheral spectrum; peripherally-multiplicative operator; spectrum-preserving map

UR - http://eudml.org/doc/269375

ER -

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