Multipliers of type (p, p) and multipliers of the groupL_p-algebras

Multipliers and the groupLp-algebras

“…Conversely, if ||/||p is finite for some / 6 L p , then-as proved in [3] f Proof. Assume that T Φ 0.…”

“…In view of Lemma 3, T is completely determined by its restriction to L p \ Thus, T may be identified with a multiplier on {Ψ(W f ): fe Lf], and so with a multiplier on its closure Ψ($l p ) in Ψ{^Jl p ) as well. It follows that T may be identified with a multiplier on 2t p , which, in view of [3], Theorem 6, may be identified with some Proof. In view of the fact that SK 2 is a C*-algebra, it follows from [5] The Supporting Institutions listed above contribute to the cost of publication of this Journal, but they are not owners or publishers and have no responsibility for its content or policies.…”

“…A function f e L p is said to be p-tempered and, as shown in [3], the number (1) ll/ll^supdl^/llpiflreCoollflrllp^l} is finite. Conversely, if ||/||p is finite for some / 6 L p , then-as proved in [3] f Proof.…”

On Multipliers of the Group Lp;w(G)-Algebras

“…) were studied and developed by McKennon [10,11,12] and Griffin [8] where the multipliers are identified as the operators commuting with the translation operators. In [3], Feichtinger showed that Banach algebra of all continuous linear operators on B which commute with left translations can be identified with the algebra of all right multipliers of the algebra of its tempered elements where B is a translation invariant Banach space of functions on locally compact groups.…”

“…In [3], Feichtinger showed that Banach algebra of all continuous linear operators on B which commute with left translations can be identified with the algebra of all right multipliers of the algebra of its tempered elements where B is a translation invariant Banach space of functions on locally compact groups. In this paper, the ideas and the methods in [2,3,[8][9][10][11][12]14,16] are used frequently for the generalization of the results of McKennon and Griffin concerning multipliers of type (p, p) to weighted Lebesgue spaces L p,w (G) for 1 ≤ p < ∞.…”