Geodesic
On Banach spaces with Mazur's property
Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 51-54

Voir la notice de l'article provenant de la source Cambridge University Press

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 E ⊗εF 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. 
Leung, Denny H. On Banach spaces with Mazur's property. Glasgow mathematical journal, Tome 33 (1991) no. 1, pp. 51-54. doi: 10.1017/S0017089500008028
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