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Varieties and Vector Measures
Author(s) -
Faires Barbara T.
Publication year - 1978
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19780850122
Subject(s) - mathematics , banach space , reflexive space , locally convex topological vector space , uniformly convex space , pure mathematics , characterization (materials science) , variety (cybernetics) , equicontinuity , approximation property , space (punctuation) , interpolation space , discrete mathematics , lp space , banach manifold , functional analysis , topological space , computer science , biochemistry , chemistry , materials science , statistics , gene , nanotechnology , operating system
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.