Translation invariant linear functionals on segal algebras

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.

Translation-invariant linear operators

The theory of translation-invariant operators on various spaces of functions (or measures or distributions) is a well-trodden field. The problem is to decide, first, whether or not a linear operator between two function spaces on, say, IR or R + which commutes with one or many translations on the two spaces is necessarily continuous, and, second, to give a canonical form for all such continuous...

Spectral Synthesis in Segal Algebras on Hypergroups

Warner (1966), Hewitt and Ross (1970), Yap (1970), and Yap (1971) extended the so-called Ditkin's condition for the group algebra L\G) of a locally compact abelian group G to the algebras L(G) Π L(G), dense subalgebras of L{G) which are essential Banach LHO-modules, LKG) Π L(G)(1 ^ p < co) and Segal algebras respectively. Chilana and Ross (1978) proved that the algebra L^K) satisfies a stronger...

On Certain Conditions for the Existence of Invariant Linear Functionals