Displaying similar documents to “Dirichlet series and uniform ergodic theorems for linear operators in Banach spaces”

On the mean ergodic theorem for Cesàro bounded operators

Yves Derriennic (2000)

Colloquium Mathematicae

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For a Cesàro bounded operator in a Hilbert space or a reflexive Banach space the mean ergodic theorem does not hold in general. We give an additional geometrical assumption which is sufficient to imply the validity of that theorem. Our result yields the mean ergodic theorem for positive Cesàro bounded operators in L p (1 < p < ∞). We do not use the tauberian theorem of Hardy and Littlewood, which was the main tool of previous authors. Some new examples, interesting for summability...

Generalized limits and a mean ergodic theorem

Yuan-Chuan Li, Sen-Yen Shaw (1996)

Studia Mathematica

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For a given linear operator L on with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on and X = , the definition of L-limit reduces to Lorentz’s definition of σ-limit, which is described by means of Banach limits on . We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version...