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1 results

  • 4 - Stein Relations and Observability Range Spaces

  • 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 103-179

  • Summary

    Chapter 4 is concerned with the state/output part of a noncommutative linear system and the range of the associated observability operator. Specifically, (i) observability operators having range landing inside of a given weighted Hardy–Fock space are characterized by the existence of a solution to certain Linear Matrix Inequality (Linear Operator Inequality in general) called a Stein inequality, (ii) conversely, subspaces of a given weighted Hardy–Fock space arising as the range of a contractive observability operator are characterized as contractively included backward-shift-invariant subspaces of the ambient Hardy–Fock space having some additional natural structural properties.