This is an announcement for the paper "The trace as an average over the unit sphere of a normed space with a 1-symmetric basis" by Tomasz Kania and Kent E. Morrison.

Abstract: We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\ell_p$-norms in $\mathbb{R}^N$ for $p\neq 2$.

Archive classification: math.FA math.CA

Mathematics Subject Classification: 15A60, 47A12

Submitted from: kmorriso@calpoly.edu

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

http://front.math.ucdavis.edu/1511.02084

or

http://arXiv.org/abs/1511.02084