A note on a theorem of Vidav
Vladimir Rakočević (2000)
Publications de l'Institut Mathématique
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Vladimir Rakočević (2000)
Publications de l'Institut Mathématique
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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...
Thaheem, A.B., Khan, A.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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David Pérez-García (2004)
Studia Mathematica
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We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
Jarno Talponen (2010)
Studia Mathematica
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We characterize Hilbert spaces among Banach spaces in terms of transitivity with respect to nicely behaved subgroups of the isometry group. For example, the following result is typical: If X is a real Banach space isomorphic to a Hilbert space and convex-transitive with respect to the isometric finite-dimensional perturbations of the identity, then X is already isometric to a Hilbert space.
Charles E. Cleaver (1972)
Colloquium Mathematicae
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Bernd Carl, Alain Pajor (1988)
Inventiones mathematicae
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S. Kwapien (1972-1973)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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David E. Edmunds, Jan Lang (2013)
Studia Mathematica
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We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.
S. Kwapień (1970)
Studia Mathematica
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R. Sztencel, P. Zaremba (1981)
Colloquium Mathematicae
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Messirdi, Bekkai, Mortad, Mohammed Hichem (2008)
Banach Journal of Mathematical Analysis [electronic only]
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Sever Silvestru Dragomir (2017)
Concrete Operators
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Some trace inequalities of Shisha-Mond type for operators in Hilbert spaces are provided. Applications in connection to Grüss inequality and for convex functions of selfadjoint operators are also given.
T. Flett (1972)
Studia Mathematica
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Akkouchi, Mohamed (2016-05-20T09:55:13Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Mecheri, Salah (2005)
Revista Colombiana de Matemáticas
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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.