Spaces of operator-valued functions measurable with respect to the strong operator topology
| dc.creator | Blasco, Oscar | |
| dc.creator | van Neerven, Jan | |
| dc.date | 2008-11-14 | |
| dc.date | 2009-04-01 | |
| dc.date.accessioned | 2026-07-07T12:58:22Z | |
| dc.date.available | 2026-07-07T12:58:22Z | |
| dc.description | Let $X$ and $Y$ be Banach spaces and $(Ω,Σ,μ)$ a finite measure space. In this note we introduce the space $L^p[μ;L(X,Y)]$ consisting of all (equivalence classes of) functions $Φ:Ω\mapsto L(X,Y)$ such that $ω\mapsto Φ(ω)x$ is strongly $μ$-measurable for all $x\in X$ and $ω\mapsto Φ(ω)f(ω)$ belongs to $L^1(μ;Y)$ for all $f\in L^{p'}(μ;X)$, $1/p+1/p'=1$. We show that functions in $L^p[μ;Ł(X,Y)]$ define operator-valued measures with bounded $p$-variation and use these spaces to obtain an isometric characterization of the space of all $L(X,Y)$-valued multipliers acting boundedly from $L^p(μ;X)$ into $L^q(μ;Y)$, $1\le q< p<\infty$. | |
| dc.description | Minor revisions; to appear in the proceedings of 3rd Meeting on Vector Measures, Integration and Applications (Eichstaett, 2008) | |
| dc.identifier | https://arxiv.org/abs/0811.2284 | |
| dc.identifier | http://arxiv.org/abs/0811.2284 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225218 | |
| dc.subject | Functional Analysis | |
| dc.subject | 28B05, 46G10 | |
| dc.title | Spaces of operator-valued functions measurable with respect to the strong operator topology | |
| dc.type | text |