Banach spaces of compact operators
Charles E. Cleaver (1972)
Colloquium Mathematicae
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Charles E. Cleaver (1972)
Colloquium Mathematicae
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Akkouchi, Mohamed (2016-05-20T09:55:13Z)
Acta Universitatis Lodziensis. Folia Mathematica
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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.
Hatamleh, Raed (2007)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94. New concepts of linear colligations and dynamic systems, corresponding to the linear operators, acting in the Banach spaces, are introduced. The main properties of the transfer function and its relation to the dual transfer function are established.
Miguel Martín, Javier Merí (2011)
Open Mathematics
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A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.
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.
Władysław Orlicz, Stanisław Szufla (1981)
Annales Polonici Mathematici
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K. Goebel, E. Złotkiewicz (1971)
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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Stanisław Szufla (2009)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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V. Lakshmikantham, A. R. Mitchell, R. W. Mitchell (1978)
Annales Polonici Mathematici
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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...
Julio Flores, Pedro Tradacete (2008)
Studia Mathematica
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It is proved that every positive Banach-Saks operator T: E → F between Banach lattices E and F factors through a Banach lattice with the Banach-Saks property, provided that F has order continuous norm. By means of an example we show that this order continuity condition cannot be removed. In addition, some domination results, in the Dodds-Fremlin sense, are obtained for the class of Banach-Saks operators.