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The Schur lemma for bounded multiplier convergent series. (English) Zbl 0494.40005


MSC:

40J05 Summability in abstract structures
40A05 Convergence and divergence of series and sequences
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References:

[1] Antosik, P., Swartz, C.: Matrix Methods in Analysis (preprint) · Zbl 0564.46001
[2] Banach, S.: Theorie des operations linéaires. Warsaw 1932 · JFM 58.1120.06
[3] Brooks, J.K.: Sur les suites uniformément convergentes dans un espace de Banach. C.R. Acad. Sci. (Paris)274, A1037-A1040 (1972) · Zbl 0226.40005
[4] Constantinescu, C.: Spaces of multipliable families in Hausdorff topological groups. In: Lecture Notes in Mathematics, Vol. 794. Berlin, Heidelberg, New York: Springer 1979 · Zbl 0428.22002
[5] Maddox, I.: Elements of functional analysis. Cambridge: Cambridge University Press · Zbl 0193.08601
[6] Pettis, B.J.: On integration in vector spaces. Trans. Am. Math. Soc.44, 277-304 (1938) · Zbl 0019.41603 · doi:10.1090/S0002-9947-1938-1501970-8
[7] Pietsch, A.: Nukleare lokalkonvexe Räume. Berlin 1965 · Zbl 0152.32302
[8] Robertson, A.: Unconditional convergence and the Vitali-Hahn-Saks theorem. Bull. Soc. Math. France, Suppl., Mem.31-32, 335-341 (1972) · Zbl 0244.46059
[9] Rolewicz, S.: Metric linear spaces, Warsaw: Polish Scientific Publishers 1972 · Zbl 0226.46001
[10] Yosida, K.: Functional analysis. Berlin, Heidelberg, New York: Springer 1966 · Zbl 0152.32102
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