Modulated and subsequential ergodic theorems in Hilbert and Banach spaces

D. Berend, M. Lin, J. Rosenblatt, Arkady Tempelman

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

Let {ak}k≥0 be a sequence of complex numbers. We obtain the necessary and sufficient conditions for the convergence of n-1k=0n ak Tkx for every contraction T on a Hilbert space H and every x ∈ H. It is shown that a natural strengthening of the conditions does not yield convergence for all weakly almost periodic operators in Banach spaces, and the relations between the conditions are exhibited. For a strictly increasing sequence of positive integers {kj}, we study the problem of when n-1j=1n Tkjx converges to a T-fixed point for every weakly almost periodic T or for every contraction in a Hilbert space and not for every weakly almost periodic operator.

Original languageEnglish (US)
Pages (from-to)1653-1665
Number of pages13
JournalErgodic Theory and Dynamical Systems
Volume22
Issue number6
DOIs
StatePublished - Dec 1 2002

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Ergodic Theorem
Hilbert spaces
Banach spaces
Almost Periodic
Hilbert space
Banach space
Contraction
Mathematical operators
Monotonic increasing sequence
Strengthening
Operator
Complex number
Strictly
Fixed point
Converge
Necessary Conditions
Integer
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Berend, D. ; Lin, M. ; Rosenblatt, J. ; Tempelman, Arkady. / Modulated and subsequential ergodic theorems in Hilbert and Banach spaces. In: Ergodic Theory and Dynamical Systems. 2002 ; Vol. 22, No. 6. pp. 1653-1665.
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Modulated and subsequential ergodic theorems in Hilbert and Banach spaces. / Berend, D.; Lin, M.; Rosenblatt, J.; Tempelman, Arkady.

In: Ergodic Theory and Dynamical Systems, Vol. 22, No. 6, 01.12.2002, p. 1653-1665.

Research output: Contribution to journalArticle

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