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A study on Dunford-Pettis completely continuous like operators | M. Alikhani
; | Date: |
2 May 2019 | Abstract: | In this article, the class of all Dunford-Pettis $ p $-convergent operators
and $ p $-Dunford-Pettis relatively compact property on Banach spaces are
investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y
$ such that the class of bounded linear operators from $ X$ to $ Y $ and some
its subspaces have the $ p $-Dunford-Pettis relatively compact property. In
addition, if $ Omega $ is a compact Hausdorff space, then we prove that
dominated operators from the space of all continuous functions from $ K $ to
Banach space $ X $ (in short $ C(Omega,X) $) taking values in a Banach space
with the $ p $-$ (DPrcP) $ are $ p $-convergent when $ X $ has the
Dunford-Pettis property of order $ p.$ Furthermore, we show that if $
T:C(Omega,X)
ightarrow Y $ is a strongly bounded operator with representing
measure $ m:Sigma
ightarrow L(X,Y) $ and $ hat{T}:B(Omega,X)
ightarrow Y $
is its extension, then $ T$ is Dunford-Pettis $ p $-convergent if and only if $
hat{T}$ is Dunford-Pettis $ p $-convergent. | Source: | arXiv, 1905.1007 | Services: | Forum | Review | PDF | Favorites |
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