Strongly and weakly almost periodic linear maps on semigroup algebras

Г-invariant operators associated with locally compact groups

“…T is said to be weakly almost periodic if the set { s T t ; (s, t) ∈ Γ} of translates of T is relatively compact with respect to weak operator topology on the set B(L ∞ (G)) of bounded linear operators from L ∞ (G) to L ∞ (G), [8]. (ii) There is a non-zero weakly almost periodic linear operator T in M Γ (L ∞ (G)).…”

On character amenability of semigroup algebras

“…Let M (S) be the Banach algebra of all bounded regular Borel measures on S with norm and convolution product [5]. Recall that M a (S) denotes the space of all measures μ ∈ M (S) on S for which the mappings x → δ x * |μ| and x → |μ| * δ x (where δ x denotes the point mass at x for x ∈ S) from S into M (S) are weakly continuous (see [1], [11] and [19]). This algebra was first studied in the sequence of papers by A. C. and J. W. Baker, [3] and [4].…”