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3 results

  • 7 - Orthogonal Beurling–Lax Representations Based on Wandering Subspaces

  • Joseph A. Ball, Vladimir Bolotnikov, College of William and Mary, Virginia
  • Book:
    Noncommutative Function-Theoretic Operator Theory and Applications
    Published online:
    09 December 2021
    Print publication:
    16 December 2021, pp 230-284

  • Summary

    Chapter 7 obtains a Beurling–Lax representation for an isometrically included forward-shift-invariant subspace of a weighted Hardy–Fock space which involves a whole family of Bergman-inner-like multipliers (rather than a single inner multiplier) which leads to an orthogonal decomposition of the forward-shift-invariant subspace. The Bergman-inner family can be viewed as the transfer-function family for a time-varying noncommutative, multidimensional weighted-conservative input/state/output linear system, and can be viewed as a time-varying isometric multiplier from a time-varying unweighted Hardy–Fock space to the given weighted Hardy–Fock space.

  • INVARIANT SUBSPACES IN THE BIDISC AND WANDERING SUBSPACES

  • Part of
  • TAKAHIKO NAKAZI
  • Journal:
    Journal of the Australian Mathematical Society / Volume 84 / Issue 3 / June 2008
    Published online by Cambridge University Press:
    01 June 2008, pp. 367-374
    Print publication:
    June 2008
    • Article
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  • Let M be a forward-shift-invariant subspace and N a backward-shift-invariant subspace in the Hardy space H2 on the bidisc. We assume that . Using the wandering subspace of M and N, we study the relations between M and N. Moreover we study M and N using several natural operators defined by shift operators on H2.