On some properties of Banach operators.
Thaheem, A.B., Khan, Abdul Rahim (2001)
International Journal of Mathematics and Mathematical Sciences
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Thaheem, A.B., Khan, Abdul Rahim (2001)
International Journal of Mathematics and Mathematical Sciences
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R. Dudley (1970)
Studia Mathematica
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J. Väisälä (1992)
Studia Mathematica
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We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.
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...
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.
Charles E. Cleaver (1972)
Colloquium Mathematicae
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Saccoman, John J. (2001)
International Journal of Mathematics and Mathematical Sciences
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Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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V. Rakočević (1984)
Matematički Vesnik
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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.
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). ...
Julio Becerra Guerrero, A. Rodríguez-Palacios (2002)
Extracta Mathematicae
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Gajek, L., Jachymski, J., Zagrodny, D. (1995)
Journal of Applied Analysis
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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.
Akkouchi, Mohamed (2016-05-20T09:55:13Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Jianlian Cui, Jinchuan Hou (2002)
Studia Mathematica
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We show that every spectrally bounded linear map Φ from a Banach algebra onto a standard operator algebra acting on a complex Banach space is square-zero preserving. This result is used to show that if Φ₂ is spectrally bounded, then Φ is a homomorphism multiplied by a nonzero complex number. As another application to the Hilbert space case, a classification theorem is obtained which states that every spectrally bounded linear bijection Φ from ℬ(H) onto ℬ(K), where H and K are infinite-dimensional...
Nygaard, Olav (2002)
International Journal of Mathematics and Mathematical Sciences
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