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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 ...

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-to-Hardy composition operators

Evgueni Doubtsov, Andrei Petrov (2013)

Open Mathematics

Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.

Borel methods of summability and ergodic theorems

Ryszard Jajte (2002)

Annales Polonici Mathematici

Passing from Cesàro means to Borel-type methods of summability we prove some ergodic theorem for operators (acting in a Banach space) with spectrum contained in ℂ∖(1,∞).

Borel parts of the spectrum of an operator and of the operator algebra of a separable Hilbert space

Piotr Niemiec (2012)

Studia Mathematica

For a linear operator T in a Banach space let σ p ( T ) denote the point spectrum of T, let σ p , n ( T ) for finite n > 0 be the set of all λ σ p ( T ) such that dim ker(T - λ) = n and let σ p , ( T ) be the set of all λ σ p ( T ) for which ker(T - λ) is infinite-dimensional. It is shown that σ p ( T ) is σ , σ p , ( T ) is σ δ and for each finite n the set σ p , n ( T ) is the intersection of an σ set and a δ set provided T is closable and the domain of T is separable and weakly σ-compact. For closed densely defined operators in a separable Hilbert space a more detailed decomposition...

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