Minimal Projections with Respect to Numerical Radius

Authors

Asuman Güven Aksoy, Claremont McKenna CollegeFollow

Document Type

Book Chapter

Department

Mathematics (CMC)

Publication Date

2016

Abstract

In this paper we survey some results on minimality of projections with respect to numerical radius. We note that in the cases L^p, 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 l^p 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.

Rights Information

© 2016 Springer International Publishing Switzerland

DOI

10.1007/978-3-319-27842-1_1

Recommended Citation

A. G. Aksoy, G. Lewicki, Minimal projections with respect to numerical radius, Ordered Structures and Applications: Positivity VII, Trends in Mathematics, pp. 1-11, 2016.