Barrelledness and bornological conditions on spaces of vector-valued μ-simple functions |
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Authors: | Santiago Diaz Lech Drewnowski Antonio Fernandez Miguel Florencio Pedro J Paul |
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Institution: | 1. E. S. Ingenieros Industriales, Avda. Reina Mercedes s/n, 41012, Sevilla, Spain 2. Inst. Matematyki, Uniw. Adama Mickiewicza, ul. Matejki 48/49, 60-769, Poznań, Poland
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Abstract: | Let S(μ, E) be the space of (classes of μ-a.e. equal) simple functions defined on a (non-trivial) measure space with values in a locally convex space E. The following results hold: S(μ,E) is quasi-barrelled (resp. bornological) if and only if E is quasi-barrelled (resp. bornological) and E′(β(E′,E)) has the property (B) of Pietsch; S(μ, E) is barrelled if and only if S(μ,K) is barrelled and E is barrelled and nuclear; S(μ, E) is never ultrabornological; and S(μ, E) is a DF-space if and only if E is a DF-space. |
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