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On Banach spaces with Mazur’s property. (English) Zbl 0745.46021

A Banach space \(E\) is said to have Mazur’s property if every weak* sequentially continuous functional in the dual \(E''\) is weak*continuous, i.e., belongs to \(E\). In this paper generalizations of some results of T. Kappeler [Math. Z. 191, 623-631 (1986; Zbl 0658.46010)] are given. These concern the stability of Mazur’s property with respect to the formation of tensor products; in particular, it is shown that the spaces \(E\overline\otimes_ \varepsilon F\) and \(L^ p(\mu,E)\) inherit Mazur’s property from \(E\) and \(F\) under some suitable conditions. Further, Mazur’s property is stable also under the formation of Schauder decompositions and some unconditional sums of Banach spaces.

MSC:

46B20 Geometry and structure of normed linear spaces
46B22 Radon-Nikodým, Kreĭn-Milman and related properties
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
46B28 Spaces of operators; tensor products; approximation properties
46M05 Tensor products in functional analysis

Citations:

Zbl 0658.46010
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References:

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