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The Dual of the Compressed Shift

Part of: General theory of linear operators Function theory on the disc

Published online by Cambridge University Press:  17 April 2020

M. C. Câmara  and
W. T. Ross
M. C. Câmara
Affiliation:
Departamento de Matematica, Instituto Superior Tecnico, 1049-001Lisboa, Portugal e-mail: cristina.camara@tecnico.ulisboa.pt
W. T. Ross*
Affiliation:
Department of Mathematics and Computer Science, University of Richmond, Richmond, VA23173, USA
*
e-mail: wross@richmond.edu
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Abstract

For an inner function u, we discuss the dual operator for the compressed shift $P_u S|_{{\mathcal {K}}_u}$, where ${\mathcal {K}}_u$ is the model space for u. We describe the unitary equivalence/similarity classes for these duals as well as their invariant subspaces.

Keywords

Inner functionsHardy spacescompressed shiftunitary equivalencesimilarityinvariant subspaces

MSC classification

Primary: 47A15: Invariant subspaces
Secondary: 47A65: Structure theory 30J05: Inner functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 1 , March 2021 , pp. 98 - 111
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

This work was partially supported by FTC/Portugal through the grant UID/MAT/04459/2019. The second author would like to thank the Center for Mathematical Analysis, Geometry, and Dynamical Systems for their hospitality where the initial research for this paper was done.

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