Noncommutative Gelfand Duality and Applications I: The Existence of invariant subspaces
Operator Algebras
2008-11-13 v1 Functional Analysis
Abstract
Gelfand duality between unital commutative C*-algebras and Compact Hausdorff spaces is extended to all unital C*-algebras, where the dual objects are what we call compact Hausdorff quantum spaces. We apply this result to obtain, a characterization of unitary groups of C*-algebras, and, for arbitrary bounded Hilbert space operators, (i) A spectral theorem cum continuous functional calculus, and (ii) A proof of the general Invariant Subspace Theorem. Also described is a nonabelian generalization of Pontryagin duality of abelian locally compact groups.
Keywords
Cite
@article{arxiv.0811.1824,
title = {Noncommutative Gelfand Duality and Applications I: The Existence of invariant subspaces},
author = {Mukul S. Patel},
journal= {arXiv preprint arXiv:0811.1824},
year = {2008}
}