Topological spectrum of elements in topological algebras

[摘要] Properties of the sets of left, right, and two-sided topologically quasi-invertible elements, topological spectra, andtopological spectral radii of elements in (not necessarily unital or commutative) topological algebras are studied. We prove thespectral mapping theorem for the topological spectrum of elements in commutative complex (not necessarily unital) topologicalalgebras and show that the topological spectral radius (as a map) is a submultiplicative seminorm in a topological algebra with afunctional topological spectrum.

[学科分类] 化学（综合）

[关键词] topological algebra;topological spectrum of an element;F-algebra;continuity of quasi-invertion;functional;topological spectrum.