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A Note on the Analytic Complete Continuity Property

✍ Scribed by Shangquan Bu

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 68 KB
Volume: 265
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7714

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✦ Synopsis

We show that a Banach space X has the analytic complete continuity property if and only if for every 1 ≤ p < ∞ and for every f ∈ H p X , the sequence f r n e i• is p-Pettis-Cauchy for every r n ↑ 1. This allows us to show that X has the analytic complete continuity property if and only if L p X has this property for every 1 ≤ p < ∞ and for every σ-finite measure space ( µ).

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