[Banach] Abstract of a paper by Lorenzo Cavallina

This is an announcement for the paper "Non-trivial translation-invariant valuations on $L^\infty$" by Lorenzo Cavallina.

Abstract: Translation-invariant valuations on the space $L^\infty(\mathbb{R}^n)$ are examined. We prove that such functionals vanish on functions with compact support. Moreover a rich family of non-trivial translation-invariant valuations on $L^\infty(\mathbb{R}^n)$ is constructed through the use of ultrafilters on $\mathbb{R}$.

Archive classification: math.FA

Mathematics Subject Classification: 46E30 (52B45)

Remarks: 23 pages, 2 figures

Submitted from: cava@ims.is.tohoku.ac.jp

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1505.00089

or

http://arXiv.org/abs/1505.00089