Unordered Baire-like vector-valued function spaces | Zendy

J. C. Ferrando | Zendy

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Unordered Baire-like vector-valued function spaces

Author(s) -

J. C. Ferrando

Publication year - 1995

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1103408756

Subject(s) - baire space , baire category theorem , mathematics , baire measure , function space , function (biology) , pure mathematics , algebra over a field , biology , evolutionary biology

In this paper we show that if I is an index set and Xi an ormed space for each i2 I, then the ‘p-direct sum (i2IXi)p; 1 p1, is UBL (unordered Baire-like) if and only if Xi;i2 I ,i s UBL. IfX is a normed UBL space and (; ;) is a nite measure space we also investigate the UBL property of the Lebesgue-Bochner spaces Lp(;X), with 1 p< 1. In what follows (; ;) will be a nite measure space and X a normed space. As usual, Lp(;X); 1 p< 1, will denote the linear space over the eld K of the real or complex numbers of all X-valued -measurable p-Bochner integrable (classes of) functions dened on , provided with the norm

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