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Tensor Algebras, Induced Representations, and the Wold Decomposition

  Published:1999-08-01
 Printed: Aug 1999
  • Paul S. Muhly
  • Baruch Solel
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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 tensor algebras, correspondence, induced representation, Wold decomposition, Beurling's theorem
MSC Classifications: 46L05, 46L40, 46L89, 47D15, 47D25, 46M10, 46M99, 47A20, 47A45, 47B35 show english descriptions General theory of $C^*$-algebras
Automorphisms
Other ``noncommutative'' mathematics based on $C^*$-algebra theory [See also 58B32, 58B34, 58J22]
unknown classification 47D15
unknown classification 47D25
Projective and injective objects [See also 46A22]
None of the above, but in this section
Dilations, extensions, compressions
Canonical models for contractions and nonselfadjoint operators
Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
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]
 

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