Isometries of Hilbert space valued function spaces

Details Isometries of Hilbert space valued function spaces Isometries of Hilbert space valued function spaces

1994-11-16

arxiv.org/abs/math/9411210v1

Mathematics

Functional Analysis

Scientific paper

Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize surjective isometries of $X(H).$ We prove that if $T$ is such an isometry then there exist Borel maps $a:\Om\to\bbK$ and $\sigma:\Om\lra\Om$ and a strongly measurable operator map $S$ of $\Om$ into $\calB(H)$ so that for almost all $\om$ $S(\om)$ is a surjective isometry of $H$ and for any $f\in X(H)$ $$Tf(\om)=a(\om)S(\om)(f(\sigma(\om))) \text{ a.e.}$$ As a consequence we obtain a new proof of characterization of surjective isometries in complex rearrangement-invariant function spaces.

Affiliated with

Also associated with

No associations

Rating

Isometries of Hilbert space valued function spaces 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 Isometries of Hilbert space valued function spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Isometries of Hilbert space valued function spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-465884