# Toeplitz operators and calculus

Zwart, Hans (2012) Toeplitz operators and calculus. Journal of functional analysis, 263 (1). pp. 167-182. ISSN 0022-1236

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 Abstract: Let be the generator of a strongly continuous, exponentially stable, semigroup on a Hilbert space. Furthermore, let the scalar function be bounded and analytic on the left-half plane, i.e., . By using the Toeplitz operator associated to , we construct an infinite-time admissible output operator . If is rational, then this operator is bounded, and equals the "normal" definition of . Although in general may be unbounded, we always have that multiplied by the semigroup is a bounded operator for every positive time instant. Furthermore, when there exists an admissible output operator such that is exactly observable, then is bounded for all with , i.e., there exists a bounded -calculus. Moreover, we rediscover some well-known classes of generators also having a bounded -calculus. Item Type: Article Copyright: © 2012 Elsevier Faculty: Electrical Engineering, Mathematics and Computer Science (EEMCS) Research Group: Link to this item: http://purl.utwente.nl/publications/80269 Official URL: http://dx.doi.org/10.1016/j.jfa.2012.04.001 Export this item as: BibTeXEndNoteHTML CitationReference Manager

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