Article contents
Central Idempotent Measures on Unitary Groups
Published online by Cambridge University Press: 20 November 2018
Extract
Let G be a locally compact group and M(G) the space of finite regular Borel measures on G. If μ and v are in M(G), their convolution is defined by
Thus, if f is a continuous bounded function on G,
μ is central if μ(Ex) = μ(xE) for all x ∈ G and all measurable sets E. μ is idempotent if μ * μ = μ.
The idempotent measures for abelian groups have been classified by Cohen [1]. In this paper we will show that for a certain class of compact groups, containing the unitary groups, the central idempotents can be characterized. The method consists of showing that, in these cases, the central idempotents arise from idempotents on abelian groups and applying Cohen's result.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1970
References
- 11
- Cited by