Non-Archimedean Gel'fand theory

Jesus M. Dominguez
1983 Pacific Journal of Mathematics  
In this paper we show that if X is a Banach algebra and X Q is its Gelfand subalgebra, then the set Xξ of the elements in X o with compact spectrum is a Gelf and algebra whose maximal ideal space is compact in the Gelίand topology. We also give a representation theorem for Xξ 9 which we use to derive the Van der Put characterization of C-algebras.
doi:10.2140/pjm.1983.104.337 fatcat:6d3uxqxrdfa23plaebkecgnj3y