Abstract
The notion of hermiticity, in complex Banach \(^{*}\)-algebras, is related to the existence of a certain order structure. We also show that any hermitian Banach algebra, containing at least one self-adjoint element whose spectrum is not an interval, contains necessarily algebraic zero-divisors. Some consequences are given.
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Nejjari, M.A. Some characterizations of hermitian Banach algebras. Rend. Circ. Mat. Palermo, II. Ser 66, 295–301 (2017). https://doi.org/10.1007/s12215-016-0253-y
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DOI: https://doi.org/10.1007/s12215-016-0253-y