Noncommmutative Gelfand Duality for not necessarily unital C*-algebras, Jordan Canonical form, and the existence of invariant subspaces
Mukul S. Patel
Abstract
Gelfand-Naimark duality (Commutative C*-algebras Locally compact Hausdorff spaces) is extended to C*-algebras Quotient maps on locally compact Hausdorff spaces. Using this duality, we give for an arbitrary bounded operator on a complex Hilbert space of several dimensions, a functional calculus and the existence theorem for nontrivial invariant subspace.
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