Minimal projections with respect to various norms
Volume 210 / 2012
Studia Mathematica 210 (2012), 1-16
MSC: Primary 41A35, 41A65; Secondary 47A12.
DOI: 10.4064/sm210-1-1
Abstract
A theorem of Rudin permits us to determine minimal projections not only with respect to the operator norm but with respect to various norms on operator ideals and with respect to numerical radius. We prove a general result about $N$-minimal projections where $N$ is a convex and lower semicontinuous (with respect to the strong operator topology) function and give specific examples for the cases of norms or seminorms of $p$-summing, $p$-integral and $p$-nuclear operator ideals.
