Pełczyński's property () of order <i>p</i> and its quantification

Abstract

Abstract We introduce the concepts of Pełczyński's property ( V ) of order p and Pełczyński's property of order p . It is proved that, for each , the James p ‐spaces enjoys Pełczyński's property of order p and the James ‐spaces (where denotes the conjugate number of p ) enjoys Pełczyński's property ( V ) of order p . We prove that both (μ a finite positive measure) and l 1 enjoy a quantitative version of Pełczyński's property .