Integral Equations and Operator Theory

, Volume 40, Issue 2, pp 231–243

The Weiss conjecture on admissibility of observation operators for contraction semigroups

  • Birgit Jacob
  • Jonathan R. Partington
Article

DOI: 10.1007/BF01301467

Cite this article as:
Jacob, B. & Partington, J.R. Integr equ oper theory (2001) 40: 231. doi:10.1007/BF01301467

Abstract

We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that\(\parallel C\left( {sI - A} \right)^{ - 1} \parallel \leqslant M\sqrt {\operatorname{Re} s} \) for alls in the open right half-plane. HereA denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators.

MSC

Primary 93C15, 47D06Secondary 47B35, 32A37

Copyright information

© Birkhäuser Verlag 2001

Authors and Affiliations

  • Birgit Jacob
    • 1
  • Jonathan R. Partington
    • 1
  1. 1.School of MathematicsUniversity of LeedsLeedsUK