Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 11-19 |
| Number of pages | 9 |
| Journal | Positivity |
| Volume | 23 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 |
Keywords
- Conditional expectations in L (μ; L (ν; X))
- Dual of L (μ; L (ν; X))
- Radon–Nikodým property
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Cite this
Lü, Q., & van Neerven, J. (2019). On conditional expectations in L p (μ; L q (ν; X)). Positivity, 23(1), 11-19. https://doi.org/10.1007/s11117-018-0589-y