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A condition equivalent to uniform ergodicity

Maria Elena Becker (2005)

Studia Mathematica

Let T be a linear operator on a Banach space X with for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) converges uniformly; (ii) .

A general differentiation theorem for multiparameter additive processes

Ryotaro Sato (2002)

Colloquium Mathematicae

Let be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and be a strongly continuous locally bounded d-dimensional semigroup of positive linear operators on L. Under suitable conditions on the Banach lattice L we prove a general differentiation theorem for locally bounded d-dimensional processes in L which are additive with respect to the semigroup T.

A general differentiation theorem for superadditive processes

Ryotaro Sato (2000)

Colloquium Mathematicae

Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=: t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.

A note on the powers of Cesàro bounded operators

Zoltán Léka (2010)

Czechoslovak Mathematical Journal

In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies

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