Almost uniform and strong convergences in ergodic theorems for symmetric spaces View Full Text


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Article Info

DATE

2019-02

AUTHORS

V. Chilin, S. Litvinov

ABSTRACT

Let (Ω,μ) be a σ-finite measure space, and let X⊂L1(Ω)+L∞(Ω) be a fully symmetric space of measurable functions on (Ω,μ). If μ(Ω)=∞, necessary and sufficient conditions are given for almost uniform convergence in X (in Egorov’s sense) of Cesàro averages Mn(T)(f)=1n∑k=0n-1Tk(f) for all Dunford–Schwartz operators T in L1(Ω)+L∞(Ω) and any f∈X. If (Ω,μ) is quasi-non-atomic, it is proved that the averages Mn(T) converge strongly in X for each Dunford–Schwartz operator T in L1(Ω)+L∞(Ω) if and only if X has order continuous norm and L1(Ω) is not contained in X. More... »

PAGES

1-25

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10474-018-0872-1

DOI

http://dx.doi.org/10.1007/s10474-018-0872-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107186518


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