Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras is an *-isomorphism.
@article{bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_61-68,
author = {Rachid ElHarti and Mohamed Mabrouk},
title = {Vector space isomorphisms of non-unital reduced Banach *-algebras},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {69},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_61-68}
}
Rachid ElHarti; Mohamed Mabrouk. Vector space isomorphisms of non-unital reduced Banach *-algebras. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 69 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2015_69_2_61-68/
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