This is an announcement for the paper "Spaces of operator-valued functions measurable with respect to the strong operator topology" by Oscar Blasco and Jan van Neerven.
Abstract: Let $X$ and $Y$ be Banach spaces and $(\Omega,\Sigma,\mu)$ a finite measure space. In this note we introduce the space $L^p[\mu;L(X,Y)]$ consisting of all (equivalence classes of) functions $\Phi:\Omega \mapsto L(X,Y)$ such that $\omega \mapsto \Phi(\omega)x$ is strongly $\mu$-measurable for all $x\in X$ and $\omega \mapsto \Phi(\omega)f(\omega)$ belongs to $L^1(\mu;Y)$ for all $f\in L^{p'}(\mu;X)$, $1/p+1/p'=1$. We show that functions in $L^p[\mu;\L(X,Y)]$ 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 $L^p(\mu;X)$ into $L^q(\mu;Y)$, $1\le q< p<\infty$.
Archive classification: math.FA
Mathematics Subject Classification: 28B05, 46G10
Remarks: 12 pages
The source file(s), Blasco_vanNeerven/BlascoVanNeerven.tex: 40452 bytes Blasco_vanNeerven/newsymbol.sty: 440 bytes Blasco_vanNeerven/srcltx.sty: 6955 bytes, is(are) stored in gzipped form as 0811.2284.tar.gz with size 14kb. The corresponding postcript file has gzipped size 97kb.
Submitted from: J.M.A.M.vanNeerven@tudelft.nl
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