On noncommutative weighted local ergodic theorems on L p -spaces

Farrukh Mukhamedov, Abdusalom Karimov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the present paper we consider a von Neumann algebra M with a faithful normal semi-finite trace τ, and {α t }, a strongly continuous extension to L p (M, τ) of a semigroup of absolute contractions on L 1(M, τ). By means of a non-commutative Banach Principle we prove for a Besicovitch function b and x ε L p (M, τ), that the averages 1/T ∫ 0 T b(t)α t (x)dt converge bilateral almost uniformly in L p (M, τ) as T → 0.

Original languageEnglish
Pages (from-to)223-235
Number of pages13
JournalPeriodica Mathematica Hungarica
Volume55
Issue number2
DOIs
Publication statusPublished - Nov 2007
Externally publishedYes

Keywords

  • Besicovitch function
  • Local ergodic theorem
  • The Banach Principle

ASJC Scopus subject areas

  • General Mathematics

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