Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗
In this paper, we study weakly compact left multipliers on the Banach algebra LUC(G) ∗ . We show that G is compact if and only if there exists a non-zero weakly compact left multipliers on LUC(G) ∗ . We also investigate the relation between positive left weakly completely continuous elements...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Islamic Azad University
2014-03-01
|
| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/128/141 |
| Summary: | In this paper, we study weakly compact left multipliers on
the Banach algebra LUC(G)
∗
. We show that G is compact if and only
if there exists a non-zero weakly compact left multipliers on LUC(G)
∗
.
We also investigate the relation between positive left weakly completely
continuous elements of the Banach algebras LUC(G)
∗
and L
∞(G)
∗
. Finally,
we prove that G is finite if and only if there exists a non-zero multiplicative
linear functional µ on LUC(G) such that µ is a left weakly
completely continuous elements of LUC(G)
∗
. |
|---|---|
| ISSN: | 1735-8299 1735-8299 |