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...
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| Format: | Article |
| Language: | English |
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Islamic Azad University
2014-03-01
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| Series: | Journal of Mathematical Extension |
| Online Access: | http://ijmex.com/index.php/ijmex/article/view/128/141 |
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doaj-5951717810834da288e9b4dae9e31a612020-11-25T01:21:33ZengIslamic Azad UniversityJournal of Mathematical Extension1735-82991735-82992014-03-0181110Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗M. J. Mehdipour0Shiraz University of TechnologyIn 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) ∗ .http://ijmex.com/index.php/ijmex/article/view/128/141 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. J. Mehdipour |
| spellingShingle |
M. J. Mehdipour Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ Journal of Mathematical Extension |
| author_facet |
M. J. Mehdipour |
| author_sort |
M. J. Mehdipour |
| title |
Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ |
| title_short |
Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ |
| title_full |
Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ |
| title_fullStr |
Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ |
| title_full_unstemmed |
Weakly Completely Continuous Elements of the Banach Algebra LUC(G) ∗ |
| title_sort |
weakly completely continuous elements of the banach algebra luc(g) ∗ |
| publisher |
Islamic Azad University |
| series |
Journal of Mathematical Extension |
| issn |
1735-8299 1735-8299 |
| publishDate |
2014-03-01 |
| description |
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)
∗
. |
| url |
http://ijmex.com/index.php/ijmex/article/view/128/141 |
| work_keys_str_mv |
AT mjmehdipour weaklycompletelycontinuouselementsofthebanachalgebralucg |
| _version_ |
1725129534666178560 |