The Path to Gelfand Duality & Spectral Theory
We provide an introduction to Banach Algebras and C*-algebras. The discussion of C*-algebras leads to the two central theorems of this thesis: Gelfand Duality & the Gelfand-Naimark-Segal (GNS) Theorem. The latter tells us that every C*-algebra may be treated as some (special) subalgebra of bounded endomorphisms of a C-Hilbert space, while the former tells us that every commutative C*-algebra c
