ArticleOriginal scientific text
Title
Vector space isomorphisms of non-unital reduced Banach *-algebras
Authors ,
Abstract
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.
Keywords
Reduced Banach algebras, preserving the spectrum.
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Main language of publication
English
Published
2015
Published online
2015-12-30
Exact and natural sciences