Modulated and subsequential ergodic theorems in Hilbert and Banach spaces

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

Research output: Contribution to journalArticle

20 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Modulated and subsequential ergodic theorems in Hilbert and Banach spaces'. Together they form a unique fingerprint.

  • Cite this