Varieties and Vector Measures | Zendy

Faires Barbara T. | Zendy

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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.

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