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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 s u p | | T / n w | | < for some 0 ≤ w < 1. We show that the following conditions are equivalent: (i) n - 1 k = 0 n - 1 T k converges uniformly; (ii) c l ( I - T ) X = z X : l i m n k = 1 n T k z / k e x i s t s .

A general differentiation theorem for multiparameter additive processes

Ryotaro Sato (2002)

Colloquium Mathematicae

Let ( L , | | · | | L ) be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and T = T ( u ) : u = ( u , . . . , u d ) , u i > 0 , 1 i d 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 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 T on a Hilbert space with a single spectrum satisfies lim n T n + 1 - T n = 0 .

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