Weakly compact multipliers on Banach algebras related to a locally compact group

Abstract

We study weakly compact left and right multipliers on the Banach algebra L ∞ 0 (G) * of a locally compact group G. We prove that G is compact if and only if L ∞ 0 (G) * has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L ∞ 0 (G) * . We also give a description of weakly compact multipliers on L ∞ 0 (G) * in terms of weakly completely continuous elements of L ∞ 0 (G) * . Finally we show that G is finite if and only if there exists a multiplicative linear functional n on L ∞ 0 (G) such that n is a weakly completely continuous element of L ∞ 0 (G) * .

The Acceptance of Mobile Health Services by Physicians: The Case of Iran

“…Then T is a weakly compact right multiplier on L ∞ (G) * . So T = ρ φ for some φ ∈ L 1 (G); see [15]. A similar argument to the proof of Theorem 4.1 shows that φ ∈ Z(L 1 (G)).…”

On character amenability of semigroup algebras

“…For μ ∈ M a (S), define T μ ∈ B M a (S) by T μ (ν) = ν * μ − χ(ν)μ. More information about bounded operators on semigroup algebras and group algebras can be found in [12] and [23]. where closure is taken in the τ K -topology.…”