Minimal projections with respect to various norms

TL;DR

This paper extends Rudin's theorem to identify minimal projections under various norms, including quasi-norms and numerical radius, broadening the understanding of projection optimization in operator theory.

Contribution

It generalizes Rudin's theorem to encompass quasi-norms and numerical radius, providing new tools for analyzing minimal projections in different operator ideals.

Findings

Minimal projections can be characterized using Rudin's theorem under various norms.

The approach applies to quasi-norms in operator ideals.

Numerical radius minimization is also addressed.

Abstract

We will show that a theorem of Rudin \cite{wr1}, \cite{wr}, permits us to determine minimal projections not only with respect to the operator norm but with respect to quasi-norms in operators ideals and numerical radius in many concrete cases.