Some results on S-numerical range of operator matrices

Abstract

A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of the Hilbert space. In this paper, we found an approximation of the S-numerical range of bounded and unbounded operator matrices by variation methods. Applications to Hain-L st operator and Stokes operator are given.

Keywords

• S-numerical range; projection method; Schro ̈dinger operator; Hain-Lu ̈st operator; Stokes operator.