Continuity of operators on Saks spaces
Iwo Labuda (1974)
Studia Mathematica
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Iwo Labuda (1974)
Studia Mathematica
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Philippe Turpin (1978)
Annales de l'institut Fourier
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An Orlicz-Pettis type property for vector measures and also the “Uniform Boundedness Principle” are shown to fail without local convexity assumption. The author asks under which generalized convexity hypotheses these properties remain true. This problem is expressed in terms of barrelledness type conditions.
K. Sundaresan (1969)
Studia Mathematica
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M. Rao (1970)
Studia Mathematica
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Michael M. Neumann (1991)
Czechoslovak Mathematical Journal
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Lech Drewnowski, Iwo Labuda (2000)
Studia Mathematica
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The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series in a topological vector space X is called ℒ-convergent if each of its lacunary subseries (i.e. those with ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density...
J. Uhl (1967)
Studia Mathematica
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J. J. Uhl Jr. (1969)
Rendiconti del Seminario Matematico della Università di Padova
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