Displaying similar documents to “On the mean ergodic theorem for Cesàro bounded operators”

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...