Iterates of a product of conditional expectation operators

Guy Cohen

doi:10.1016/j.jfa.2006.09.008

Iterates of a product of conditional expectation operators

Guy Cohen

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Let (Ω, F, μ) be a probability space and let T = P₁ P₂ ⋯ P_d be a finite product of conditional expectations with respect to the sub σ-algebras F₁, F₂, ..., F_d. We show that for every f ∈ L_p (μ), 1 < p ≤ 2, the sequence {Tⁿ f} converges μ-a.e., withunder(lim, n → ∞) Tⁿ f = E [f | F₁ ∩ F₂ ∩ ⋯ ∩ F_d] μ -a.e.

Original language	English
Pages (from-to)	658-668
Number of pages	11
Journal	Journal of Functional Analysis
Volume	242
Issue number	2
DOIs	https://doi.org/10.1016/j.jfa.2006.09.008
State	Published - 15 Jan 2007
Externally published	Yes

Keywords

Almost everywhere convergence
Cesàro summability
Complex interpolation
Conditional expectations
Maximal inequality
Spectral sets

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2006.09.008

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title = "Iterates of a product of conditional expectation operators",

abstract = "Let (Ω, F, μ) be a probability space and let T = P1 P2 ⋯ Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1, F2, ..., Fd. We show that for every f ∈ Lp (μ), 1 < p ≤ 2, the sequence {Tn f} converges μ-a.e., withunder(lim, n → ∞) Tn f = E [f | F1 ∩ F2 ∩ ⋯ ∩ Fd] μ -a.e.",

keywords = "Almost everywhere convergence, Ces{\`a}ro summability, Complex interpolation, Conditional expectations, Maximal inequality, Spectral sets",

author = "Guy Cohen",

note = "Funding Information: 1 The author was partially supported by Israel Science Foundation grant 1333/04.",

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N2 - Let (Ω, F, μ) be a probability space and let T = P1 P2 ⋯ Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1, F2, ..., Fd. We show that for every f ∈ Lp (μ), 1 < p ≤ 2, the sequence {Tn f} converges μ-a.e., withunder(lim, n → ∞) Tn f = E [f | F1 ∩ F2 ∩ ⋯ ∩ Fd] μ -a.e.

AB - Let (Ω, F, μ) be a probability space and let T = P1 P2 ⋯ Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1, F2, ..., Fd. We show that for every f ∈ Lp (μ), 1 < p ≤ 2, the sequence {Tn f} converges μ-a.e., withunder(lim, n → ∞) Tn f = E [f | F1 ∩ F2 ∩ ⋯ ∩ Fd] μ -a.e.

KW - Almost everywhere convergence

KW - Cesàro summability

KW - Complex interpolation

KW - Conditional expectations

KW - Maximal inequality

KW - Spectral sets

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SP - 658

EP - 668

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Iterates of a product of conditional expectation operators

Abstract

Keywords

ASJC Scopus subject areas

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