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    Borodulin-Nadzieja, Piotr and Plebanek, Grzegorz 2010. On sequential properties of Banach spaces, spaces of measures and densities. Czechoslovak Mathematical Journal, Vol. 60, Issue. 2, p. 381.


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    Plebanek, Grzegorz 1995. Compact spaces that result from adequate families of sets. Topology and its Applications, Vol. 65, Issue. 3, p. 257.


    Schlüchtermann, G. 1992. The Mazur property and completeness in the space of Bochner-integrable functions L1(μ, X). Glasgow Mathematical Journal, Vol. 34, Issue. 02, p. 201.


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On Banach spaces with Mazur's property

  • Denny H. Leung (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500008028
  • Published online: 01 May 2009
Abstract

A Banach space E is said to have Mazur's property if every weak* sequentially continuous functional in E” is weak* continuous, i.e. belongs to E. Such spaces were investigated in [5] and [9] where they were called d-complete and μB-spaces respectively. The class of Banach spaces with Mazur's property includes the WCG spaces and, more generally, the Banach spaces with weak* angelic dual balls [4, p. 564]. Also, it is easy to see that Mazur's property is inherited by closed subspaces. The main goal of this paper is to present generalizations of some results of [5] concerning the stability of Mazur's property with respect to forming some tensor products of Banach spaces. In particular, we show in Sections 2 and 3 that the spaces EεF and Lp(μ, E) inherit Mazur's property from E andF under some conditions. In Section 4, we will also show the stability of Mazur's property under the formation of Schauder decompositions and some unconditional sums of Banach spaces.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

2.J. Diestel and J. J. Uhl Jr, Vector measures, Math. Surveys no. 15 (American Math. Soc., 1977).

3.L. Drewnowski , On Banach spaces with the Gelfand-Phillips property, Math. Z. 193 (1986), 405411.

4.G. Edgar , Measurability in a Banach space, II, Indiana Univ. Math. J. 28 (1979), 559579.

5.T. Kappeler , Banach spaces with the condition of Mazur, Math. Z. 191 (1986), 623631.

6.H. H. Schaefer , Topological vector spaces, Graduate Texts in Mathematics no. 3 (Springer1971).

7.H. H. Schaefer ,Banach lattices and positive operators, Die Grundlehren der Mathematischen Wissenschaften no. 215 (Springer, 1974).

9.A. Wilansky , Mazur spaces, Intemat. J. Math. Sci. 4 (1981), 3953.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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