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Barrelledness of the space of vector valued and simple functions. (English) Zbl 0525.46022


MSC:

46E40 Spaces of vector- and operator-valued functions
46A08 Barrelled spaces, bornological spaces
46M05 Tensor products in functional analysis
28A33 Spaces of measures, convergence of measures
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References:

[1] Diestel, J., Uhl, J.J., Jr. Vector measures. Mathematical Surveys, No. 15. Providence: American Mathematical Society 1977 · Zbl 0369.46039
[2] Freniche, F.J.: The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property (preprint) · Zbl 0529.28004
[3] Grothendieck A.: Produits tensoriels topologiques et espaces nucléaires. Memoirs of the American Mathematical Society, No. 16. Providence: American Mathematical Society 1955
[4] Jarchow, H.: Locally convex spaces. Mathematische Leitfäden. Stuttgart: Teubner 1981 · Zbl 0466.46001
[5] Mendoza, J.: Barrelledness conditions onS(?,E) andB(?,E). Math. Ann.261, 11-22 (1982) · Zbl 0487.46010 · doi:10.1007/BF01456405
[6] Nissenzweig, A.:w *-sequential convergence. Israel J. Math.22, 266-272 (1975) · Zbl 0341.46012 · doi:10.1007/BF02761594
[7] Pietsch, A.: Nuclear locally convex spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete 66. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0308.47024
[8] Schachermayer, W.: On some classical measure-theoretic theorems for non sigma-complete Boolean algebras. Überarbeitete Fassung des Institutsberichtes, 120. Linz-Auhof: Johannes-Kepler-Universität Linz 1980 · Zbl 0522.28007
[9] Semadeni, Z.: Banach spaces of continuous functions. Pa?stwowe Wydawnictwo Naukowe: Warszawa 1971
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