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Conditions for Admissibility of Observation Operators and Boundedness of Hankel Operators |
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| Authors: | |
| Institution: | (1) Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany;(2) School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK;(3) Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK |
| Abstract: | We derive new necessary and sufficient conditions for admissibility
of observation operators for certain C
0-semigroups. We also prove a new
sufficient criterion for admissibility for observation operators with infinite-dimensional
output space on contraction semigroups. If the contraction semigroup
is completely non-unitary and its co-generator has finite defect indices,
then this criterion is also necessary. In the case of the right shift semigroup
on L
2(0, ), these conditions translate into conditions for the boundedness
of Hankel operators. |
| Keywords: | 47D06 32A37 93B28 |
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