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.
Andreas Defant, Mieczysław Mastyło (2003)
Studia Mathematica
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The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.
Teresa Alvarez (1988)
Publicacions Matemàtiques
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In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l.
Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner (2001)
Studia Mathematica
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Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).
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.
Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)
Colloquium Mathematicae
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We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X). ...
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.
V. Rakočević (1984)
Matematički Vesnik
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H. G. Dales, Tomasz Kania, Tomasz Kochanek, Piotr Koszmider, Niels Jakob Laustsen (2013)
Studia Mathematica
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Alfonso Montes-Rodríguez, M. Carmen Romero-Moreno (2002)
Studia Mathematica
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We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that...
Nicole Tomczak (1970)
Studia Mathematica
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Jerry Johnson, John Wolfe (1979)
Studia Mathematica
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Luis Bernal-González (2017)
Open Mathematics
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In this paper, a criterion for the existence of large linear algebras consisting, except for zero, of one-to-one operators on an infinite dimensional Banach space is provided. As a consequence, it is shown that every separable infinite dimensional Banach space supports a commutative infinitely generated free linear algebra of operators all of whose nonzero members are one-to-one. In certain cases, the assertion holds for nonseparable Banach spaces.
Kislyakov, S.V., Maksimov, D.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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Niels Jacob (1990)
Forum mathematicum
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