Sequentially Right Banach spaces of order p

Mahdi Dehghani; Mohammad B. Dehghani; Mohammad S. Moshtaghioun

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 1, page 51-67
  • ISSN: 0010-2628

Abstract

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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 ≤ p ≤ ∞ . 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.

How to cite

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Dehghani, Mahdi, Dehghani, Mohammad B., and Moshtaghioun, Mohammad S.. "Sequentially Right Banach spaces of order $p$." Commentationes Mathematicae Universitatis Carolinae 61.1 (2020): 51-67. <http://eudml.org/doc/297335>.

@article{Dehghani2020,
abstract = {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\le p\le \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.},
author = {Dehghani, Mahdi, Dehghani, Mohammad B., Moshtaghioun, Mohammad S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
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 $p$},
language = {eng},
number = {1},
pages = {51-67},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sequentially Right Banach spaces of order $p$},
url = {http://eudml.org/doc/297335},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Dehghani, Mahdi
AU - Dehghani, Mohammad B.
AU - Moshtaghioun, Mohammad S.
TI - Sequentially Right Banach spaces of order $p$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 1
SP - 51
EP - 67
AB - 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\le p\le \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.
LA - eng
KW - 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 $p$
UR - http://eudml.org/doc/297335
ER -

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