Minimal Numerical-Radius Extensions of Operators
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 Lp, 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.
© 2007 American Mathematical Society
A. Aksoy, B. L. Chalmers, “Minimal numerical-radius extensions of operators,” Proc. of Amer. Math. Soc.135 (2007), No. 4, 1039-1050.