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Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

We study whether the operator space V * * ⊗ α W * * can be identified with a subspace of the bidual space ( V ⊗ α W ) * * , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.

Biequivalence vector spaces in the alternative set theory

Miroslav Šmíd, Pavol Zlatoš (1991)

Commentationes Mathematicae Universitatis Carolinae

As a counterpart to classical topological vector spaces in the alternative set theory, biequivalence vector spaces (over the field Q of all rational numbers) are introduced and their basic properties are listed. A methodological consequence opening a new view towards the relationship between the algebraic and topological dual is quoted. The existence of various types of valuations on a biequivalence vector space inducing its biequivalence is proved. Normability is characterized in terms of total...

Bilinear operators and limiting real methods

Fernando Cobos, Alba Segurado (2014)

Banach Center Publications

We investigate the behaviour of bilinear operators under limiting real methods. As an application, we show an interpolation formula for spaces of linear operators. Some results on norm estimates for bounded linear operators are also established.

Bi-Lipschitz embeddings of hyperspaces of compact sets

Jeremy T. Tyson (2005)

Fundamenta Mathematicae

We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ℝ n + 1 ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...

Bilipschitz invariance of the first transverse characteristic map

Michel Hilsum (2012)

Banach Center Publications

Given a smooth S¹-foliated bundle, A. Connes has shown the existence of an additive morphism ϕ from the K-theory group of the foliation C*-algebra to the scalar field, which factorizes, via the assembly map, the Godbillon-Vey class, which is the first secondary characteristic class, of the classifying space. We prove the invariance of this map under a bilipschitz homeomorphism, extending a previous result for maps of class C¹ by H. Natsume.

Binomial-Poisson entropic inequalities and the M/M/∞ queue

Djalil Chafaï (2006)

ESAIM: Probability and Statistics

This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group ...

Binormality of Banach spaces

Petr Holický (1997)

Commentationes Mathematicae Universitatis Carolinae

We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space ℓ ∞ is not binormal.

Biorthogonal systems in Banach spaces

Michael A. Coco (2004)

Studia Mathematica

We give biorthogonal system characterizations of Banach spaces that fail the Dunford-Pettis property, contain an isomorphic copy of c₀, or fail the hereditary Dunford-Pettis property. We combine this with previous results to show that each infinite-dimensional Banach space has one of three types of biorthogonal systems.

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