Journal article
Composition Operators and Endomorphisms
Complex analysis and operator theory, Vol.6(1), pp.163-188
02/01/2012
DOI: 10.1007/s11785-010-0075-4
Abstract
If b is an inner function, then composition with b induces an endomorphism, beta, of L-infinity(T) that leaves H-infinity(T) invariant. We investigate the structure of the endomorphisms of B(L-2(T)) and B(H-2(T)) that implement beta through the representations of L-infinity(T) and H-infinity(T) in terms of multiplication operators on L-2(T) and H-2(T). Our analysis, which is based on work of Rochberg and McDonald, will wind its way through the theory of composition operators on spaces of analytic functions to recent work on Cuntz families of isometries and Hilbert C*-modules.
Details
- Title: Subtitle
- Composition Operators and Endomorphisms
- Creators
- Dennis Courtney - University of IowaPaul S. Muhly - University of IowaSamuel W. Schmidt - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Complex analysis and operator theory, Vol.6(1), pp.163-188
- DOI
- 10.1007/s11785-010-0075-4
- ISSN
- 1661-8254
- eISSN
- 1661-8262
- Publisher
- Springer Nature
- Number of pages
- 26
- Grant note
- DMS-0602242 / University of Iowa Department of Mathematics NSF VIGRE
- Language
- English
- Date published
- 02/01/2012
- Academic Unit
- Statistics and Actuarial Science; Mathematics
- Record Identifier
- 9984397938202771
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