Noncommmutative Gelfand Duality for not necessarily unital $C^*$-algebras, Jordan Canonical form, and the existence of invariant subspaces
Abstract
Description
Gelfand-Naimark duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to $C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces. Using this duality, we give for an \emph{arbitrary} bounded operator on a complex Hilbert space of several dimensions, a functional calculus and the existence theorem for nontrivial invariant subspace.
Under consideration for publication by Electronic Reasearch Announcements of the AMS
Under consideration for publication by Electronic Reasearch Announcements of the AMS