A Limit Theorem for Discrete Quantum Groups
Mehrdad Kalantar

TL;DR
This paper proves that for discrete quantum groups, the convolution powers of an irreducible state diminish to zero in strong operator topology, extending classical limit theorems to the quantum setting.
Contribution
It establishes a limit theorem for convolution powers on discrete quantum groups, generalizing classical results to the quantum group framework.
Findings
Convolution powers of irreducible states tend to zero in strong operator topology.
The result applies to discrete quantum groups and their associated completely positive maps.
Extends classical limit theorems to the quantum group context.
Abstract
We consider the {\it concentration functions problem} for discrete quantum groups; we prove that if is a discrete quantum group, and is an irreducible state in , then the convolution powers , considered as completely positive maps on , converge to zero in strong operator topology.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Algebraic structures and combinatorial models · Advanced Topics in Algebra
