Real Banach \(*\) algebras
The systematic study of real Banach *-algebras are given in this paper. It is shown that \textit{J. W. M. Ford}'s lemma [see J. Lond. Math. Soc. 42, 521-522 (1967; Zbl 0145.38702)] and \textit{V. Pták}'s inequality [see Bull. Lond. Math. Soc. 2, 327-334 (1970; Zbl 0209.44403)] hold in the real case and the (real) linear span of unitary elements contains all skew-hermitian elements. Moreover, main properties of symmetric real Banach *-algebras, of *-representations and topologically irreducible *-representations of real Banach *-algebras, of *-radical of real Banach *-algebras, of the enveloping real \(C^*\)-algebras of a hermitian real Banach *-algebra and of the real state space of a hermitian real Banach*-algebra without identity are described.
scientific article; zbMATH DE number 1530092
scientific article