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m-Berezin transform and compact operators.

Kyesook Nam, Dechao Zheng, Changyong Zhong (2006)

Revista Matemática Iberoamericana

m-Berezin transforms are introduced for bounded operators on the Bergman space of the unit ball. The norm of the m-Berezin transform as a linear operator from the space of bounded operators to L∞ is found. We show that the m-Berezin transforms are commuting with each other and Lipschitz with respect to the pseudo-hyperbolic distance on the unit ball. Using the m-Berezin transforms we show that a radial operator in the Toeplitz algebra is compact iff its Berezin transform vanishes on the boundary...

Mean ergodicity for compact operators

Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan (2003)

Studia Mathematica

A mean ergodic theorem is proved for a compact operator on a Banach space without assuming mean-boundedness. Some related results are also presented.

Measure of noncompactness of linear operators between spaces of sequences that are ( N ¯ , q ) summable or bounded

Eberhard Malkowsky, V. Rakočević (2001)

Czechoslovak Mathematical Journal

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are ( N ¯ , q ) summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y . Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.

Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie

Valerie Girardin (1997)

Studia Mathematica

We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.

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