Spectral Theory on Unital Commutative full Symmetric Krein C*-Algebras

Abstract

An involutive algebra (A,*) is called a Krein C*-algebra if it admits at least on eBanach algebra norm and one fundamental symmetry of (A, *), i.e., α ϵ Aut(A,*) such that α² = 1[subscript A] and ||α(x)*x|| = | ||² for all x ϵ A. The ultimate goal is to develop a spectral theory on unital commutative Krein C*-algebras when the odd part is a symmetric imprimitivity bimodule over the even part and there exists a suitable "exchange symmetry" ε between A₊ and A₋. The result we obtained is a generalization of spectral theory on unital commutative C*-algebras