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- Title
C<sup>*</sup>-Subalgebras Generated by a Single Operator in B( H).
- Authors
Cho, Ilwoo; Jorgensen, Palle E. T.
- Abstract
In this paper, we characterize a C*-subalgebra C*( x) of B( H), generated by a single operator x. We show that if x is polar-decomposed by aq, where a is the partial isometry part and q is the positive operator part of x, then C*( x) is *-isomorphic to the groupoid crossed product algebra $\mathcal{A}_{q}\times_{\alpha }\mathbb{G}_{a}$ , where $\mathcal{A}_{q}=C^{*}(q)$ and $\mathbb{G}_{a}$ is the graph groupoid induced by a partial isometry part a of x.
- Subjects
CROSS product (Mathematics); DIRECTED graphs; GROUPOIDS; LINEAR operators; HILBERT space; SPECTRAL theory; COMPUTATIONAL mathematics; SYMBOLIC dynamics
- Publication
Acta Applicandae Mathematicae, 2009, Vol 108, Issue 3, p625
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-009-9478-5