arXiv subjects

J. Alejandro Chávez-Domínguez

Publications and source records attributed to J. Alejandro Chávez-Domínguez.

2 recordsLinked to original sources

arXiv2016

Unconditionally $p$-converging operators and Dunford-Pettis Property of order $p$

In the present paper we study unconditionally $p$-converging operators and Dunford-Pettis property of order $p$. New characterizations of unconditionally $p$-converging operators and Dunford-Pettis property of order $p$ are established. Six quantities are defined to measure how far an operator is from being unconditionally $p$-converging. We prove quantitative versions of relationships of completely continuous operators,unconditionally $p$-converging operators and unconditionally converging operators. We further investigate possible quantifications of the Dunford-Pettis property of order $p$.

math.FA↗

arXiv2016

Pełczyński's property ($V^{*}$) of order $p$ and its quantification

We introduce the concepts of Pełczyński's property ($V$) of order $p$ and Pełczyński's property ($V^{*}$) of order $p$. It is proved that, for each $1<p<\infty$, the James $p$-space $J_{p}$ enjoys Pełczyński's property ($V^{*}$) of order $p$ and the James $p^{*}$-space $J_{p^{*}}$ (where $p^{*}$ denotes the conjugate number of $p$) enjoys Pełczyński's property ($V$) of order $p$. We prove that both $L_{1}(μ)$ ($μ$ a finite positive measure) and $l_{1}$ enjoy the quantitative version of Pełczyński's property ($V^{*}$).

math.FA↗