On (V) and (V*) sets in vector valued function spaces



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Bombal Gordón, Fernando (1991) On (V) and (V*) sets in vector valued function spaces. In Function spaces : proceedings of the Second International Conference, Poznań 1989, August 28-September 2. Teubner-Texte zur Mathematik (120). Teubner, Stuttgart, pp. 80-89. ISBN 3815420210


A. Pełczyński [Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641–648; defined and studied the properties (V) and (V*), proving that if a Banach space E [resp. its conjugate E∗] has property (V) then E∗ [resp. E] has property (V*), and asking whether the converse implications are true. It is known that the answer to Pełczyński's question is negative; E. Saab and P. Saab, Pacific J. Math. 125 (1986), no. 1, 205–210. The first part of this paper is concerned with the problem of characterizing Banach spaces for which the answer to Pełczyński's question is positive.
The second part is devoted to a study of (V)- and (V*)-subsets and the heredity of (V)- and (V*)-properties for the Banach space C(Ω,E).

Item Type:Book Section
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International Conference "Function Spaces" (2. 1989. Poznan, Polonia)

Uncontrolled Keywords:continuous E-valued functions; supnorm topology; (V)-set; weakly relatively compact subsets
Subjects:Sciences > Mathematics > Topology
ID Code:19887
Deposited On:11 Feb 2013 14:43
Last Modified:11 Feb 2013 14:43

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