Weakly regular topological algebras and spectral extension property
Keywords:topological algebra, weakly regular algebra, spectral extension property
Properties of weakly regular topological algebras are examined. Necessary and sufficient conditions for a commutative semisimple spectral algebra to have the spectral extension property for semisimple algebras is given. Some applications are also considered concerning the automatic continuity, unique uniform norm property and existence of algebra norms on topological algebras with functional spectrum.