Spaces of operator-valued functions measurable with respect to the strong operator topology

Details Spaces of operator-valued functions measurable with respect to the strong operator topology Spaces of operator-valued functions measurable with respect to the strong operator topology

2008-11-14

arxiv.org/abs/0811.2284v2

Mathematics

Functional Analysis

Minor revisions; to appear in the proceedings of 3rd Meeting on Vector Measures, Integration and Applications (Eichstaett, 200

Scientific paper

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 $L^q(\mu;Y)$, $1\le q< p<\infty$.

Affiliated with

Also associated with

No associations

Rating

Spaces of operator-valued functions measurable with respect to the strong operator topology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spaces of operator-valued functions measurable with respect to the strong operator topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spaces of operator-valued functions measurable with respect to the strong operator topology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-10877