We define concepts of amenability and coamenability for algebraic quantum groups in the sense of Van Daele (1998). We show that coamenability of an algebraic quantum group always implies amenability ...of its dual. Various necessary and/or sufficient conditions for amenability or coamenability are obtained. Coamenability is shown to have interesting consequences for the modular theory in the case that the algebraic quantum group is of compact type.
The analytic rank of a $C\sp $-algebra Murphy, Gerard J.
Proceedings of the American Mathematical Society,
03/1992, Volume:
115, Issue:
3
Journal Article
The Analytic Rank of a C-Algebra Murphy, Gerard J.
Proceedings of the American Mathematical Society,
07/1992, Volume:
115, Issue:
3
Journal Article
Peer reviewed
A concept of rank for unital C*-algebras, which reduces to the dimension of the spectrum in the case of separable abelian C*-algebras, is introduced. This rank has properties somewhat similar to the ...stable rank, but it appears to be easier to compute in many cases. It is very well behaved with respect to tensor products and crossed products with countable discrete abelian groups.
We give characterizations of Toeplitz operators on generalised H
2 spaces and derive some properties of the corresponding Toeplitz algebras. The proofs depend essentially on having a "sufficient" ...supply of inner functions.
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