Compact homomorphisms between uniform Fréchet algebras

• DOI: 10.1007/s00574-016-0110-9
• Publication Date: 2016-02-17T07:10:45Z
• Authors: Cicero Nachtigall; Daniela M. Vieira
• Keywords: Algebra homomorphism; Banach algebra

We study compact homomorphisms between uniform Frechet algebras, by analyzing the behavior of its spectral adjoint on the underlying spectrum. We prove that every compact homomorphism between uniform Frechet algebras actually ranges into a uniform Banach algebra, and that its spectral adjointmaps τ-bounded subsets into relatively τ-compact subsets, when τ is the strong or the compact-open topology.