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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Thaheem, A.B., Khan, A.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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M. Kadec (1971)
Studia Mathematica
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El-Shobaky, Entisarat, Ali, Sahar Mohammed, Takahashi, Wataru (2001)
Abstract and Applied Analysis
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Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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Wilansky, A. (1979)
Portugaliae mathematica
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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). ...
Kalton, N.J. (2005)
The New York Journal of Mathematics [electronic only]
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M. Mathieu, G. J. Schick (2002)
Studia Mathematica
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A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ Mr(x) for all x ∈ E, where r(·) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.
Åsvald Lima, Eve Oja (1999)
Studia Mathematica
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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E). ...
Joram Lindenstrauss (1975-1976)
Séminaire Choquet. Initiation à l'analyse
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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}.