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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.

Biseparating maps on generalized Lipschitz spaces

Denny H. Leung (2010)

Studia Mathematica

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are characterized...

Bloch type spaces on the unit ball of a Hilbert space

Zhenghua Xu (2019)

Czechoslovak Mathematical Journal

We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

bm-independence and central limit theorems associated with symmetric cones

Janusz Wysoczański (2007)

Banach Center Publications

We present a generalization of the classical central limit theorem to the case of non-commuting random variables which are bm-independent and indexed by a partially ordered set. As the set of indices I we consider discrete lattices in symmetric positive cones, with the order given by the cones. We show that the limit measures have moments which satisfy recurrences generalizing the recurrence for the Catalan numbers.

BMO and Lipschitz approximation by solutions of elliptic equations

Joan Mateu, Yuri Netrusov, Joan Orobitg, Joan Verdera (1996)

Annales de l'institut Fourier

We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak * spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.

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