Àlgebres de Banach i el teorema de Gelfand-Naimark

Abstract

[en] Banach algebras are Banach spaces equipped with a continuous multiplication. We begin this thesis by familiarizing ourselves with the general theory of these objects. Next, we turn our attention to the study of the commutative case. It is in this frame that we conclude the project, by proving the Gelfand-Naimark theorem, a striking representation theorem of a certain type of Banach algebras, namely commutative C*-algebras.