Convolution semigroups of states.

Lindsay, Martin and Skalski, Adam G. (2011) Convolution semigroups of states. Mathematische Zeitschrift, 267 (1-2). pp. 325-339. ISSN 1432-1823

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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.

Item Type:
Journal Article
Journal or Publication Title:
Mathematische Zeitschrift
Additional Information:
15 pages. Preprint, 24 June 2009. Published Online First™, 3 November 2009. The original publication is available at
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Deposited On:
22 Nov 2010 09:32
Last Modified:
21 Nov 2022 20:09