ε-Numerical Range of Operator Polynomial

Relying on some ideas of numerical ranges, we introduce, for operators polynomials on a complex Hilbert space, a new notion called the ε -numerical range of operators polynomials. Some geometrical and topological properties of these ε -numerical range are proved. Thereby, we achieve a new characterization of ε -numerical range of operators polynomials on an arbitrary Hilbert space. All our results are new even for n × n -matrix polynomials.