Pełczyński's property (V∗) of order p and its quantification

• Published in: Mathematische Nachrichten Vol. 291; no. 2-3; pp. 420 - 442
• Main Authors: Li, Lei, Chen, Dongyang, Chávez‐Domínguez, Javier Alejandro
• Format: Journal Article
• Language: English
• Published: 01-02-2018
• Subjects: 46‐B; Pełczyński’s property (V) of order p; Pełczyński’s property (V∗) of order p; quantitative Pełczyński’s property (V∗) of order p
• ISSN: 0025-584X; 1522-2616
• DOI: 10.1002/mana.201600335

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<∞, the James p‐spaces Jp enjoys Pełczyński's property (V∗) of order p and the James p∗‐spaces Jp∗ (where p∗ denotes the conjugate number of p) enjoys Pełczyński's property (V) of order p. We prove that both L1(μ) (μ a finite positive measure) and l1 enjoy a quantitative version of Pełczyński's property (V∗).