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Non-commutative martingale VMO-spaces

Narcisse Randrianantoanina (2009)

Studia Mathematica

We study Banach space properties of non-commutative martingale VMO-spaces associated with general von Neumann algebras. More precisely, we obtain a version of the classical Kadets-Pełczyński dichotomy theorem for subspaces of non-commutative martingale VMO-spaces. As application we prove that if ℳ is hyperfinite then the non-commutative martingale VMO-space associated with a filtration of finite-dimensional von Neumannn subalgebras of ℳ has property (u).

Nonseparability of the quotient space cabv(∑,m;X)/L¹(m;X) for Banach spaces X without the Radon-Nikodym property

Lech Drewnowski (1993)

Studia Mathematica

It is shown that if (S,∑,m) is an atomless finite measure space and X is a Banach space without the Radon-Nikodym property, then the quotient space cabv(∑,m;X)/L¹(m;X) is nonseparable.

Normal Structure of Banach Spaces.

W.L. Bynum (1973/1974)

Manuscripta mathematica

Norms for copulas.

Darsow, William F., Olsen, Elwood T. (1995)

International Journal of Mathematics and Mathematical Sciences

Norms in product spaces which preserve approximation properties.

Carlos Benítez, Manuel Fernández (1986)

Extracta Mathematicae

Norms that locally depend on countably many linear functionals.

M. Fabian, V. Zizler (2001)

Extracta Mathematicae

Note on a Banach space having equal linear dimension with is second dual.

Anatolij Plichko, M. Wójtowicz (2003)

Extracta Mathematicae

Note on distortion and Bourgain ℓ₁-index

Anna Maria Pelczar (2009)

Studia Mathematica

Relations between different notions measuring proximity to ℓ₁ and distortability of a Banach space are studied. The main result states that a Banach space all of whose subspaces have Bourgain ℓ₁-index greater than $ω^{α}$ , α < ω₁, contains either an arbitrarily distortable subspace or an $ℓ ₁^{α}$ -asymptotic subspace.

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