Abstract
A locally convex space L has the property ℰ if equicontinuous subsets of L* are weak-star sequentially compact. (L*, σ(L*, L)) is a MAZUR space if given F ∈ L** with F weak-star sequentially continuous then F∈ L. If L is complete with the property ∈, then (L*, σ (L*, L)) is a MAZUR space. The class of locally convex spaces with the property ℰ forms a variety ℰ and this variety is generated by the BANACH spaces it contains. Weakly compactly generated locally convex spaces and SCHWARTZ spaces belong to ℰ. MAZUR spaces are used to give a characterization of GROTHENDIECK BANACH spaces. The last section contains a characterization of the variety generated by the reflexive BANACH spaces.
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