Abstract
Many fundamental results of the spectral theory of Banach algebras have been generalized, on one hand, to some more general associative topological algebras, for example, locally multiplicatively convex algebras (Michael 1952), locally convex algebras (Allan 1956) etc… and on the other hand, to non-associative case, like, topological jordan algebras with continuous inverse (C.Viola 1971), Banach-Jordan algebras (J.Martinez Moreno 1977) and non-commutative Banach-Jordan algebras (Kaidi 1977). The purpose of this work is to develop a spectral theory of a special class of topological Jordan algebras.
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