This is an announcement for the paper “Pełczyński's property $(V^*)$ of order $p$ and its quantification” by Lei Lihttp://arxiv.org/find/math/1/au:+Li_L/0/1/0/all/0/1, 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.
Abstract: We introduce the concepts of Pe{\l}czy'{n}ski's property $(V)$ of order $p$ and Pe{\l}czy'{n}ski's property $(V^*)$ of order $p$. It is proved that, for each $1<p<\infty$, the James $p$-space $J_p$ enjoys Pe{\l}czy'{n}ski's property $(V^*)$ of order $p$ and the James $p^*$-space $J_{p^*}$ (where $p^*$ denotes the conjugate number of $p$) enjoys Pe{\l}czy'{n}ski's property $(V)$ of order $p$. We prove that both $L_1(\mu)$ ($\mu$ a finite positive measure) and $\ell_1$ enjoy the quantitative version of Pe{\l}czy'{n}ski's property $(V^*)$.
The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1607.02163