Ali Ülger (2001)
Colloquium Mathematicae
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Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
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.
Appell, J., Väth, M., Vignoli, A. (1999)
Zeitschrift für Analysis und ihre Anwendungen
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I. Kubiaczyk, S. Szufla (1982)
Publications de l'Institut Mathématique
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Walden Freedman (2002)
Colloquium Mathematicae
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A Banach space X has property (E) if every operator from X into c₀ extends to an operator from X** into c₀; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips...
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...
Emilia Perri (1983)
Rendiconti del Seminario Matematico della Università di Padova
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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.
D. L. Grant, I. L. Reilly (1990)
Matematički Vesnik
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Danuta Ozdarska, Stanisław Szufla (1993)
Mathematica Slovaca
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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...
Tber, Moulay Hicham (2007)
APPS. Applied Sciences
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Mieczysław Cichoń (1995)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we prove a theorem for the existence of pseudo-solutions to the Cauchy problem, x' = f(t,x), x(0) = x₀ in Banach spaces. The function f will be assumed Pettis-integrable, but this assumption is not sufficient for the existence of solutions. We impose a weak compactness type condition expressed in terms of measures of weak noncompactness. We show that under some additionally assumptions our solutions are, in fact, weak solutions or even strong solutions. Thus, our theorem...