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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.

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