Multipliers and the Relative Completion in Lwp(G)

Abstract

Quek and Yap defined a relative completion A for a linear subspace A of Lp(G), 1 ≤ p < ∞ and proved that there is an isometric isomorphism, between Hom<inf>L1(G)</inf>, (L1(G), A) and Ã, where Hom<inf>L1(G)</inf>(L1(G), A) is the space of the module homomorphisms (or multipliers) from L1(G) to A. In the present, we defined a, relative completion A for a linear subspace A of L<inf>w</inf> p,(G), where w is a Beurling's weighted function and L <inf>w</inf>p(G) is the weighted Lp(G) space, ([14]). Also, we proved that there is an algeabric isomorphism and homeomorphism, between Hom<inf>Lw1(G)</inf>(L<inf>w</inf>1(G), A) and Ã. At the end of this work we gave some applications and examples. © TÜBİTAK.