Minimal Projections with Respect to Numerical Radius

Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this paper we survey some results on minimality of projections with respect to numerical radius. We note that in the cases Lp, p = 1, 2, ∞, there is no difference between the minimality of projections measured either with respect to operator norm or with respect to numerical radius. However, we give an example of a projection from lp 3 onto a two-dimensional subspace which is minimal with respect to norm, but not with respect to numerical radius for p ≠ 1, 2,∞. Furthermore, utilizing a theorem of Rudin and motivated by Fourier projections, we give a criterion for minimal projections, measured in numerical radius. Additionally, some results concerning strong unicity of minimal projections with respect to numerical radius are given.

Keywords

Numerical radius minimal projection diagonal extremal pairs Fourier projection 

Mathematics Subject Classification (2010).

Primary 41A35, 41A65 Secondary 47A12 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsClaremont McKenna CollegeClaremontUSA
  2. 2.Dept. of Math and Comp. Sci.Jagiellonian UniversityKrakówPoland

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