Convolution semigroups of states
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 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.
Cite
@article{arxiv.0905.1296,
title = {Convolution semigroups of states},
author = {J. Martin Lindsay and Adam Skalski},
journal= {arXiv preprint arXiv:0905.1296},
year = {2009}
}
Comments
15 pages; accepted for publication in Mathematische Zeitschrift. v2 contains several minor corrections, main theorems remain unchanged