Minimal Numerical-Radius Extensions of Operators

Authors

Asuman Güven Aksoy, Claremont McKenna CollegeFollow
Bruce L. Chalmers, University of California, Riverside

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2007

Abstract

In this paper we characterize minimal numerical-radius extensions of operators from finite-dimensional subspaces and compare them with minimal operator-norm extensions. We note that in the cases L^p, p = 1, ∞, and in the case of self-adjoint extensions in L², the two extensions and their norms are equal.

An analogous result is also true for an arbitrary extension. Finally, we provide an example of a projection from l ^p₃ onto a two-dimensional subspace which is minimal with respect to norm but not with respect to the numerical radius for p ≠ 1, 2,∞, and we determine the minimal numerical-radius projection in this same situation.

Rights Information

© 2007 American Mathematical Society

DOI

10.1090/S0002-9939-06-08609-6

Recommended Citation

A. Aksoy, B. L. Chalmers, “Minimal numerical-radius extensions of operators,” Proc. of Amer. Math. Soc.135 (2007), No. 4, 1039-1050.