Sequentially Right-like properties on Banach spaces
Abstract
In this paper, we first study concept $ p $-sequentially Right property, which is $ p$-version of
the sequentially Right property.\ Also,
we introduce a new class of subsets of Banach spaces which is called
$ p$-Right$ ^{\ast} $ set and obtain the relationship between p-Right subsets and p-Right$ ^{\ast} $
subsets of dual spaces.\ Furthermore, for $ 1\leq
p<q\leq\infty, $ we introduce the concepts of
properties $ (SR)_{p,q}$ and $ (SR^{\ast})_{p,q}$ in order to find a
condition which every Dunford-Pettis $ q $-convergent operator is Dunford-Pettis $p$-convergent.\ Finally, we apply these concepts and obtain
some characterizations of $ p $-Dunford-Pettis relatively compact property of Banach spaces and their dual spaces.
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