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Tensor Algebras, Induced Representations, and the Wold Decomposition

Published online by Cambridge University Press:  20 November 2018

Paul S. Muhly  and
Baruch Solel
Paul S. Muhly
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A. email: muhly@math.uiowa.edu
Baruch Solel
Affiliation:
Department of Mathematics, Technion, 32000 Haifa, Israel email: mabaruch@techunix.technion.ac.il
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Abstract

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Our objective in this sequel to $[18]$ is to develop extensions, to representations of tensor algebras over ${{C}^{*}}$-correspondences, of two fundamental facts about isometries on Hilbert space: The Wold decomposition theorem and Beurling’s theorem, and to apply these to the analysis of the invariant subspace structure of certain subalgebras of Cuntz-Krieger algebras.

Keywords

46L0546L4046L8947D1547D2546M1046M9947A2047A4547B35Tensor AlgebrasCorrespondenceInduced RepresentationWold DecompositionBeurling’s theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 4 , 01 August 1999 , pp. 850 - 880
Copyright
Copyright © Canadian Mathematical Society 1999

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