Numerical Range of Two Operators in Semi-Inner Product Spaces

In this paper, the numerical range for two operatorsboth linear and nonlinearhave 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 clo- sure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.