Translation Invariant Sigma Algebras on Groups

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 ...

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

APPROXIMATELY INNER sigma-DYNAMICS ON C* ALGEBRAS

Generalized sigma-derivation on Banach algebras

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

Translation Invariant States on Twisted Algebras on a Lattice

We construct an algebra with twisted commutation relations and equip it with the shift. For appropriate irregularity of the non-local commutation relations we prove that the tracial state is the only translation-invariant state.