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Tensor Algebras, Induced Representations, and the Wold Decomposition |
Canad. J. Math. 51(1999), 850-880
Published:1999-08-01
Printed: Aug 1999
Printed: Aug 1999
- Paul S. Muhly
- Baruch Solel
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 47D15 47D25 - unknown classification 47D25 46M10 - 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] |