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Journal of Operator Theory

Volume 82, Issue 1, Summer 2019  pp. 173-188.

Universality and models for semigroups of operators on a Hilbert space

Authors:  B. C\'elari\`es (1), I. Chalendar (2), J.R. Partington (3)
Author institution:(1) Universit\'e de Lyon, Universit\'e Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 bld du 11/11/1918, F-69622 Villeurbanne, France
(2) Universit\'e Paris-Est, LAMA, (UMR 8050), UPEM, UPEC, CNRS, F-77454, Marne-la-Vall\'ee, France
(3) School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.

Summary: This paper considers universal Hilbert space operators understood in the sense of Rota, and gives criteria for universality of semigroups in the context of uniformly continuous semigroups and contraction semigroups. Specific examples are given. Universal semigroups provide models for these classes of semigroups: following a line of research initiated by Shimorin, models for concave semigroups are developed, in terms of shifts on reproducing kernel Hilbert spaces.

Keywords: universal operator, $C_0$-semigroup, Wold-type decomposition, concave operator, reproducing kernel, Toeplitz operator

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