On uniformly smoothing stochastic operators

Wojciech Bartoszek

Displaying similar documents to “On uniformly smoothing stochastic operators”

Most Markov operators on C(X) are quasi-compact and uniquely ergodic

Ryszard Rębowski (1987)

Colloquium Mathematicae

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A remark on the range of elementary operators

Said Bouali, Youssef Bouhafsi (2010)

Czechoslovak Mathematical Journal

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Let $L (H)$ denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space $H$ into itself. Given $A \in L (H)$ , we define the elementary operator $Δ_{A} : L (H) ⟶ L (H)$ by $Δ_{A} (X) = A X A - X$ . In this paper we study the class of operators $A \in L (H)$ which have the following property: $A T A = T$ implies $A T^{*} A = T^{*}$ for all trace class operators $T \in C_{1} (H)$ . Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the fact that the ultraweak closure of the range of $Δ_{A}$ is closed...

On asymptotic cyclicity of doubly stochastic operators

Wojciech Bartoszek (1999)

Annales Polonici Mathematici

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It is proved that a doubly stochastic operator P is weakly asymptotically cyclic if it almost overlaps supports. If moreover P is Frobenius-Perron or Harris then it is strongly asymptotically cyclic.

Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel&#039;yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

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Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace $X ₀ : = x \in X : l i m_{n \to \infty} | | T ⁿ x | | = 0$ is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness $χ_{| | \cdot | | ₁} (A) < 1$ for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove...

On a theorem of H. P. Lotz on quasi-compactness of Markov operators

Wojciech Bartoszek (1987)

Colloquium Mathematicae

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Uniform exponential ergodicity of stochastic dissipative systems

Beniamin Goldys, Bohdan Maslowski (2001)

Czechoslovak Mathematical Journal

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We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in $ℝ^{d}$ with $d \leq 3$ .

Asymptotic behaviour of stochastic quasi dissipative systems

Giuseppe Da Prato (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.

Some remarks on quasi-Cohen sets

Pascal Lefèvre, Daniel Li (2001)

Colloquium Mathematicae

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We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection $C (G) / C_{E^{c}} (G) ↪ L ²_{E} (G)$ is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.