Actions of compact groups on AF $C^{\ast}$-algebras

Z-actions on AH algebras and Z-actions on AF algebras

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two Z-actions with the Rohlin property on such a C∗-algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent. We also prove that locall...

MINIMAL BRATTELI DIAGRAMS AND THE DIMENSION GROUPS OF AF Cast-ALGEBRAS

An important and widely studied class of operator algebras is the approximately finitedimensional (AF) C∗-algebras. Their name stems from the fact that each element of the algebra can be approximated, to arbitrary precision, by an element from a finitedimensional subalgebra. As such elements are direct sums of matrices, the AF algebras can be thought of as builtup from relatively simple matrix ...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Representations of Compact Groups on Banach Algebras

Let a compact group U act by automorphisms of a commutative regular and Wiener Banach algebra A. We study representations Ru of U on quotient spaces A/I(üj), where u> is an orbit of U in the Gelfand space X of A and L(uj) is the minimal closed ideal with hull w C X. The main result of the paper is: if A = AP(X) is a weighted Fourier algebra on a LCA group X = A with a subpolynomial weight p on ...

Translation-invariant Function Algebras on Compact Groups

Let X be a compact group. $(X) denotes the Banach algebra (point multiplication, sup norm) of continuous complexvalued functions on X A is any closed subalgebra of d(X) which is stable under right and left translations and contains the constants. It is shown, by means of the Peter-Weyl Theorem and some multilinear algebra, that the condition (*) every representation of degree 1 of X has finite ...