Abstract of a paper by Mukul S. Patel
This is an announcement for the paper "Noncommmutative Gelfand duality for not necessarily unital $C^*$-algebras, Jordan canonical form, and the existence of invariant subspaces" by Mukul S. Patel. Abstract: Gelfand-Naimark duality (Commutative $C^*$-algebras $\equiv$ Locally compact Hausdorff spaces) is extended to \begin{center}$C^*$-algebras $\equiv$ Quotient maps on locally compact Hausdorff spaces.\end{center} 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. Archive classification: Functional Analysis; Operator Algebras Mathematics Subject Classification: 46L05; 47A13; 47A13; 43A40; 22B05 Remarks: Under consideration for publication by Electronic Reasearch The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0508545 or http://arXiv.org/abs/math.FA/0508545 or by email in unzipped form by transmitting an empty message with subject line uget 0508545 or in gzipped form by using subject line get 0508545 to: math@arXiv.org.
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Dale Alspach