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Pełczyński's property ( V ∗ ) of order p and its quantification
Author(s) -
Li Lei,
Chen Dongyang,
ChávezDomínguez Javier Alejandro
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600335
Subject(s) - property (philosophy) , mathematics , order (exchange) , epistemology , philosophy , business , finance
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 J p enjoys Pełczyński's property ( V ∗ ) of order p and the James p ∗ ‐spaces J p ∗(where p ∗ denotes the conjugate number of p ) enjoys Pełczyński's property ( V ) of order p . We prove that bothL 1 ( μ )(μ a finite positive measure) and l 1 enjoy a quantitative version of Pełczyński's property ( V ∗ ) .