Compact right multipliers on a Banach algebra related to locally compact semigroups

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

“…Then L ∞ (G) * and L ∞ 0 (G) * are Banach algebras with the first Arens product. One can prove that L ∞ (G) * and L ∞ 0 (G) * have right identities [5,9]; for more study see [1,2,[11][12][13][14]. Let M(G) be the measure algebra of G. Then M(G) with the convolution product is a unital Banach algebra and M(G) ∼ = C 0 (G) * , where C 0 (G) is the space of all complexvalued continuous functions on G that vanish at infinity [7].…”

“…Remark 2.5 In Theorems 2.2, 2.4 and Corollary 2.3, we consider a Banach algebra A such that either eA is semisimple when A has a right identity e or A/ran(A) is semisimple. ( ) Let us remark that if G is a locally compact group, then the Banach algebras L 1 (G), M(G) and L ∞ 0 (G) * satisfy the condition ( ); For an extensive study of these Banach algebras see [8,9,10,11]. Also, C * -algebras, semisimple Banach algebras with a bounded approximate identity and Banach algebras with rad(A) = ran(A) satisfy the condition ( ).…”

“…The substitution −a for a in (8) gives 2d(a 2 ) − d(a) − 2d(ea) + d(ea 2 ) = 3ed(a) + 3ad(a) + 3ead(a). (10)Combining (9) with(10) we arrive at d(a) + 2d(ea) = 3ed(a).…”

Derivations on Convolution Algebras

“…They showed that some aspects of the theory of L ∞ (G) * when G is a compact group hold for L ∞ 0 (ω) * . Other aspects of analysis on these Banach algebras have been studied by many authors; see for example, [9,13,18].…”