location:  Publications → journals → CJM
Abstract view

# Tensor Algebras, Induced Representations, and the Wold Decomposition

Published:1999-08-01
Printed: Aug 1999
• Paul S. Muhly
• Baruch Solel
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Our objective in this sequel to \cite{MSp96a} 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: tensor algebras, correspondence, induced representation, Wold decomposition, Beurling's theorem
 MSC Classifications: 46L05 - General theory of $C^*$-algebras 46L40 - Automorphisms 46L89 - Other noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22] 47D15 - unknown classification 47D1547D25 - unknown classification 47D2546M10 - Projective and injective objects [See also 46A22] 46M99 - None of the above, but in this section 47A20 - Dilations, extensions, compressions 47A45 - Canonical models for contractions and nonselfadjoint operators 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]