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ADMISSIBLE AND WEAKLY ADMISSIBLE OBSERVATION OPERATORS FOR THE RIGHT SHIFT SEMIGROUP

Published online by Cambridge University Press:  17 June 2002

Birgit Jacob ,
Jonathan R. Partington  and
Sandra Pott
Birgit Jacob
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK (birgit@amsta.leeds.ac.uk; J.R.Partington@leeds.ac.uk)
Jonathan R. Partington
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK (birgit@amsta.leeds.ac.uk; J.R.Partington@leeds.ac.uk)
Sandra Pott
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, UK (sp23@york.ac.uk)
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Abstract

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In this note we show that two conjectures of George Weiss on admissible and weakly admissible observation operators fail to hold in general for the right shift semigroup in the case that the output space is infinite dimensional.

AMS 2000 Mathematics subject classification: Primary 47D06; 32A37; 93B28

Keywords

shift semigroupadmissibilityHankel operatorobservation operator
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 353 - 362
Copyright
Copyright © Edinburgh Mathematical Society 2002