Geodesic
Sequentially Right Banach spaces of order $p$
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 51-67 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order $p$, and those defined by the dual property, the sequentially Right$^*$ Banach spaces of order $p$ for $1\leq p\leq\infty$. These classes of Banach spaces are characterized by the notions of $L_p$-limited sets in the corresponding dual space and $R^*_p$ subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space $X$ and a reflexive Banach space $Y$ has the sequentially Right property of order $p$ when $X$ enjoys this property.
We introduce and study two new classes of Banach spaces, the so-called sequentially Right Banach spaces of order $p$, and those defined by the dual property, the sequentially Right$^*$ Banach spaces of order $p$ for $1\leq p\leq\infty$. These classes of Banach spaces are characterized by the notions of $L_p$-limited sets in the corresponding dual space and $R^*_p$ subsets of the involved Banach space, respectively. In particular, we investigate whether the injective tensor product of a Banach space $X$ and a reflexive Banach space $Y$ has the sequentially Right property of order $p$ when $X$ enjoys this property.
DOI : 10.14712/1213-7243.2020.011
Classification : 46B20, 46B25, 47L05
Keywords: Right topology; sequentially Right Banach space; pseudo weakly compact operator; Pełczyński's property (V) of order $p$; limited $p$-converging operator; $p$-Gelfand--Phillips property; reciprocal Dunford--Pettis property of order $p$ 
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     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Dehghani, Mahdi; Dehghani, Mohammad B.; Moshtaghioun, Mohammad S. Sequentially Right Banach spaces of order $p$. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 51-67. doi: 10.14712/1213-7243.2020.011

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