TY - JOUR
T1 - On conditional expectations in L p (μ; L q (ν; X))
AU - Lü, Qi
AU - van Neerven, Jan
PY - 2019
Y1 - 2019
N2 - Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L p (μ; L q (ν; X)) onto LFp(μ;Lq(ν;X)), the closed subspace in L p (μ; L q (ν; X)) of all functions having a strongly F-measurable representative.
AB - Let (A, A, μ) and (B, B, ν) be probability spaces, let F be a sub-σ-algebra of the product σ-algebra A× B, let X be a Banach space and let 1 < p, q< ∞. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to F defines a bounded linear operator from L p (μ; L q (ν; X)) onto LFp(μ;Lq(ν;X)), the closed subspace in L p (μ; L q (ν; X)) of all functions having a strongly F-measurable representative.
KW - Conditional expectations in L (μ; L (ν; X))
KW - Dual of L (μ; L (ν; X))
KW - Radon–Nikodým property
UR - http://www.scopus.com/inward/record.url?scp=85048355525&partnerID=8YFLogxK
U2 - 10.1007/s11117-018-0589-y
DO - 10.1007/s11117-018-0589-y
M3 - Article
AN - SCOPUS:85048355525
VL - 23
SP - 11
EP - 19
JO - Positivity: an international journal devoted to the theory and applications of positivity in analysis
JF - Positivity: an international journal devoted to the theory and applications of positivity in analysis
SN - 1385-1292
IS - 1
ER -