Open AccessVector space isomorphisms of non-unital reduced Banach *-algebras
Author(s) -
Rachid ElHarti,
Mohamed Mabrouk
Publication year - 2015
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2015.69.2.61-68
Subject(s) - isomorphism (crystallography) , mathematics , unital , pure mathematics , isometry (riemannian geometry) , banach space , identity (music) , simple (philosophy) , discrete mathematics , algebra over a field , crystallography , physics , crystal structure , chemistry , philosophy , epistemology , acoustics
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.