Hilbert points in Hilbert space-valued $L^p$ spaces
Peer reviewed, Journal article
Published version
View/ Open
Date
2023Metadata
Show full item recordCollections
- Institutt for matematiske fag [2359]
- Publikasjoner fra CRIStin - NTNU [37304]
Original version
North-Western European Journal of Mathematics. 2023, 9 17-29.Abstract
Let H be a Hilbert space and (Ω,F ,µ) a probability space. A Hilbert point in L p (Ω;H) is a nontrivial function ϕ such that ∥ϕ∥p ≤ ∥ϕ+f ∥p whenever ⟨f ,ϕ⟩ = 0. We demonstrate that ϕ is a Hilbert point in L p (Ω;H) for some p , 2 if and only if ∥ϕ(ω)∥H assumes only the two values 0 and C > 0. We also obtain a geometric description of when a sum of independent Rademacher variables is a Hilbert point.