Leung, Denny H. On Banach spaces with Mazur’s property. (English) Zbl 0745.46021 Glasg. Math. J. 33, No. 1, 51-54 (1991). 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. Reviewer: S.Swaminathan (Halifax) Cited in 10 Documents 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 Keywords:weak* sequentially continuous functional; stability of Mazur’s property with respect to the formation of tensor products; Schauder decompositions; unconditional sums of Banach spaces Citations:Zbl 0658.46010 PDFBibTeX XMLCite \textit{D. H. Leung}, Glasg. Math. J. 33, No. 1, 51--54 (1991; Zbl 0745.46021) Full Text: DOI References: [1] DOI: 10.1155/S0161171281000021 · Zbl 0466.46005 · doi:10.1155/S0161171281000021 [2] Schaefer, Banach lattices and positive operators (1974) · Zbl 0296.47023 · doi:10.1007/978-3-642-65970-6 [3] Schaefer, Topological vector spaces (1971) · Zbl 0212.14001 · doi:10.1007/978-1-4684-9928-5 [4] DOI: 10.1007/BF01179760 · Zbl 0491.46010 · doi:10.1007/BF01179760 [5] DOI: 10.1512/iumj.1979.28.28039 · Zbl 0418.46034 · doi:10.1512/iumj.1979.28.28039 [6] DOI: 10.1007/BF01229808 · Zbl 0629.46020 · doi:10.1007/BF01229808 [7] Diestel, Vector measures (1977) · doi:10.1090/surv/015 [8] DOI: 10.1007/BF01162352 · Zbl 0658.46010 · doi:10.1007/BF01162352 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.