Sharp estimates for conditionally centred moments and for compact\n operators on L^p spaces

2020/08/16 by Eugene Shargorodsky, Shargorodsky, Eugene, Teo Sharia +1
Mathematics · #46B20 #46B28 #46E30 #47A30 #47B07 #60E15 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2008.06925

openalex publication_date 2020/08/16 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

Let (\Ω, \F, \P) be a probability space, \ξ be a\nrandom variable on (\Ω, \F, \P), \G be a\nsub-\σ-algebra of \F, and let \E^\G =\n E(\⋅ | \G) be the corresponding conditional expectation\noperator. We obtain sharp estimates for the moments of \ξ -\n\E^\G\ξ in terms of the moments of \ξ. This allows us to\nfind the optimal constant in the bounded compact approximation property of\nL^p([0, 1]), 1 < p < \∞.\n

Citations

• Foundations of Modern Probability

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