Search: MSC category 47A67
( Representation theory )
1. CJM Online first
||Elements of $C^*$-algebras attaining their norm in a finite-dimensional representation|
We characterize the class of RFD $C^*$-algebras as those containing
a dense subset of elements that attain their norm under a finite-dimensional
representation. We show further that this subset is the whole
space precisely when every irreducible representation of the
$C^*$-algebra is finite-dimensional, which is equivalent to the
$C^*$-algebra having no simple infinite-dimensional AF subquotient.
We apply techniques from this proof to show the existence of
elements in more general classes of $C^*$-algebras whose norms
in finite-dimensional representations fit certain prescribed
Keywords:AF-telescope, RFD, projective
2. CJM Online first
||A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups|
This paper introduces a class of abstract linear representations
Banach convolution function algebras over
homogeneous spaces of compact groups. Let $G$ be a compact group
and $H$ be a closed subgroup of $G$.
Let $\mu$ be the normalized $G$-invariant measure over the compact
homogeneous space $G/H$ associated to the
Weil's formula and $1\le p\lt \infty$.
We then present a structured class of abstract linear representations
Banach convolution function algebras $L^p(G/H,\mu)$.
Keywords:homogeneous space, linear representation, continuous unitary representation, convolution function algebra, compact group, convolution, involution
Categories:43A85, 47A67, 20G05