This is an announcement for the paper “Unconditionally p-converging operators and Dunford-Pettis Property of order $p$” by Dongyang Chenhttp://arxiv.org/find/math/1/au:+Chen_D/0/1/0/all/0/1, J. Alejandro Chávez-Domínguezhttp://arxiv.org/find/math/1/au:+Ch%7Ba%7Dvez_Dom%7Bi%7Dnguez_J/0/1/0/all/0/1, Lei Lihttp://arxiv.org/find/math/1/au:+Li_L/0/1/0/all/0/1.
Abstract: 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 $p$.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1607.02161