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Convolution semigroups of states.

Research output: Contribution to journalJournal article

Published

Journal publication date02/2011
JournalMathematische Zeitschrift
Journal number1-2
Volume267
Number of pages15
Pages325-339
Original languageEnglish

Abstract

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C*-bialgebra, the noncommutative counterpart of a locally compact semigroup. On locally compact quantum groups we obtain a bijective correspondence between such convolution semigroups and a class of C_0-semigroups of maps which we characterise. On C*-bialgebras of discrete type we show that all weakly continuous convolution semigroups of states are automatically norm-continuous. As an application we deduce a known characterisation of continuous conditionally positive-definite Hermitian functions on a compact group.

Bibliographic note

15 pages. Preprint, 24 June 2009. Published Online First™, 3 November 2009. The original publication is available at www.springerlink.com