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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0033-4,
author = {Takeshi Miura and Dai Honma},
title = {A generalization of peripherally-multiplicative surjections between standard operator algebras},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {479-486},
zbl = {1197.47051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0033-4}
}
Takeshi Miura; Dai Honma. A generalization of peripherally-multiplicative surjections between standard operator algebras. Open Mathematics, Tome 7 (2009) pp. 479-486. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0033-4/
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