Logo image
Composition Operators and Endomorphisms
Journal article   Peer reviewed

Composition Operators and Endomorphisms

Dennis Courtney, Paul S. Muhly and Samuel W. Schmidt
Complex analysis and operator theory, Vol.6(1), pp.163-188
02/01/2012
DOI: 10.1007/s11785-010-0075-4
url
https://arxiv.org/pdf/1003.2806View
Open Access

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.
Mathematics Mathematics, Applied Physical Sciences Science & Technology

Details

Metrics

Logo image