Displaying similar documents to “ w * -basic sequences and reflexivity of Banach spaces”

Projections from L ( X , Y ) onto K ( X , Y )

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

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Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X * has the approximation property (respectively Y is weakly compactly generated Asplund space and Y * has the approximation property). Suppose that L ( X , Y ) ≠ K ( X , Y ) and let 1 < λ < 2 . Then X (respectively Y ) can be equivalently renormed so that any projection P of L ( X , Y ) onto K ( X , Y ) has the sup-norm greater or equal to λ . ...

Banach spaces which admit a norm with the uniform Kadec-Klee property

S. Dilworth, Maria Girardi, Denka Kutzarova (1995)

Studia Mathematica

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Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space L 2 ( Ӿ ) if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

Schauder bases and the bounded approximation property in separable Banach spaces

Jorge Mujica, Daniela M. Vieira (2010)

Studia Mathematica

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Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties s u p n ∈ ℕ | | T ₙ | | ≤ λ + ϵ and l i m s u p n → ∞ | | T ₙ | | ≤ λ . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.

A note on Banach spaces with ℓ 1 -saturated duals

Denny H. Leung (1996)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that there exists a Banach space with an unconditional basis which is not c 0 -saturated, but whose dual is ℓ 1 -saturated.

On copies of c 0 in the bounded linear operator space

Juan Carlos Ferrando, J. M. Amigó (2000)

Czechoslovak Mathematical Journal

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In this note we study some properties concerning certain copies of the classic Banach space c 0 in the Banach space ℒ X , Y of all bounded linear operators between a normed space X and a Banach space Y equipped with the norm of the uniform convergence of operators.

On bases in Banach spaces

Tomek Bartoszyński, Mirna Džamonja, Lorenz Halbeisen, Eva Murtinová, Anatolij Plichko (2005)

Studia Mathematica

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We investigate various kinds of bases in infinite-dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain complete minimal systems in ℓ ∞ as well as in separable Banach spaces.