Julio Flores, César Ruiz (2006)
Studia Mathematica
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Given a positive Banach-Saks operator T between two Banach lattices E and F, we give sufficient conditions on E and F in order to ensure that every positive operator dominated by T is Banach-Saks. A counterexample is also given when these conditions are dropped. Moreover, we deduce a characterization of the Banach-Saks property in Banach lattices in terms of disjointness.
Ju. A. Abramovič, L. P. Janovskiĭ (1982)
Colloquium Mathematicae
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J. R. Holub (1971)
Colloquium Mathematicae
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Stanisław Szufla (1977)
Annales Polonici Mathematici
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Jochen Reinermann (1970)
Annales Polonici Mathematici
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K. Goebel, E. Złotkiewicz (1971)
Colloquium Mathematicae
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V. Lakshmikantham, A. R. Mitchell, R. W. Mitchell (1978)
Annales Polonici Mathematici
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Stephen A. Saxon, Albert Wilansky (1977)
Colloquium Mathematicae
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Stanisław Szufla (2009)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Antonio S. Granero, Mar Jiménez, Alejandro Montesinos, José P. Moreno, Anatolij Plichko (2003)
Studia Mathematica
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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...
Iryna Banakh, Taras Banakh (2010)
Studia Mathematica
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We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.
Vincenzo B. Moscatelli (1973)
Publications du Département de mathématiques (Lyon)
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Gerard Buskes
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CONTENTS1. Prerequisites....................................................................................52. The history.......................................................................................63. Helly's Part.......................................................................................64. Banach's proof.................................................................................75. The shortest proof...........................................................................86....
Alistair Bird, Niels Jakob Laustsen (2010)
Banach Center Publications
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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...
Bertram Yood (2008)
Studia Mathematica
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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.