Ultraproducts in Banach space theory.
Stefan Heinrich (1980)
Journal für die reine und angewandte Mathematik
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Stefan Heinrich (1980)
Journal für die reine und angewandte Mathematik
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Peter G. Casazza, Niels J. Nielsen (2003)
Studia Mathematica
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We prove that the symmetric convexified Tsirelson space is of weak cotype 2 but not of cotype 2.
Manuel Valdivia (1975)
Journal für die reine und angewandte Mathematik
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C. Schütt (1980-1981)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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N:, Maurey, B. Ghoussoub (1989)
Journal für die reine und angewandte Mathematik
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Andrzej Kryczka (2015)
Annales UMCS, Mathematica
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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach-Saks property. We prove that if (Xν) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach-Saks property, then the deviation from the weak Banach-Saks property of an operator of a certain class between direct sums E(Xν) is equal to the supremum of such deviations attained on the coordinates Xν. This is a quantitative version for operators of...
Andrzej Kryczka (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (Xv) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(Xv) is equal to the supremum of such deviations attained on the coordinates Xv. This is a quantitative version for operators of...
Richard M. Timoney (1980)
Journal für die reine und angewandte Mathematik
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Mina Ettefagh (2012)
Colloquium Mathematicae
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We show that under some conditions, 3-weak amenability of the (2n)th dual of a Banach algebra A for some n ≥ 1 implies 3-weak amenability of A.
Gilles Pisier (1989)
Journal für die reine und angewandte Mathematik
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B.D. Malviya (1975)
Journal für die reine und angewandte Mathematik
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C. S. Barroso, M. A. M. Marrocos, M. P. Rebouças (2013)
Studia Mathematica
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We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic...
Jan Prüß (1978)
Journal für die reine und angewandte Mathematik
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Gerhard Grimeisen (1974)
Journal für die reine und angewandte Mathematik
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S. Dineen, M. Klimek, R.M. Timoney (1988)
Journal für die reine und angewandte Mathematik
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D. P. Sinha, K. K. Arora (1997)
Collectanea Mathematica
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