Numerical Range of Two Operators in Semi-Inner Product Spaces

Abstract

In this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operators. We also show the inclusion relation between approximate point spectrum and closure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.