Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (4): 467-.

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MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES

 Cenap Duyar A. Turan G¨urkanli   


  1. Department of Mathematics, Faculty of Arts and Science, Ondokuz Mayis University,
    55139 Kurupelit Samsun, Turkey
  • Online:2003-10-06 Published:2003-10-06

Abstract:

Let $G$ be a locally compact Abelian group with
Haar measure $\mu $. In the present paper, first the authors
discussed some properties of weighted Lorentz space. Then they
defined the relative completion $\tilde {A}$ of a subspace $A$ of
the weighted Lorentz space, and showed that the space of the
multipliers from $L_{w}^{1} (G)$ to $A$ is algebrically isomorphic
and homeomorphic to $\tilde {A}$.

Key words: Banach module, weighted Lp(G) space, Lorentz space, weighted Lorentz
space, multiplier

CLC Number: 

  • 43A15
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