Turkish Journal of Mathematics
Abstract
Quek and Yap defined a relative completion à for a linear subspace A of L^p(G), 1 \leq p < \infty ; and proved that there is an isometric isomorphism, between Hom_{L^1(G)}(L^1(G), A) and Ã, where Hom_{L^1(G)}(L^1(G),A) is the space of the module homomorphisms (or multipliers) from L^1(G) to A. In the present, we defined a relative completion à for a linear subspace A of L_w^p(G) ,where w is a Beurling's weighted function and L_w^p(G) is the weighted L^p(G) space, ([14]). Also, we proved that there is an algeabric isomorphism and homeomorphism, between Hom_{L_w^1(G)} (L_w^1(G),A) and Ã. At the end of this work we gave some applications and examples.
DOI
-
Keywords
Module homomorphism (or multiplier), relative completion, essential module, weighted L^p(G) space. 1991 AMS subject classification codes 43
First Page
181
Last Page
191
Recommended Citation
DUYAR, CENAP and GÜRKANLI, A. TURAN (2007) "Multipliers and the Relative Completion in L_w^p(G)," Turkish Journal of Mathematics: Vol. 31: No. 2, Article 6. Available at: https://journals.tubitak.gov.tr/math/vol31/iss2/6
