A characterization of S-pseudospectra of linear operators in a Hilbert space

In this work, we introduce and study the S-pseudospectra of linear operators defined by nonstrict inequality in a Hilbert space. Inspired A. B?ttcher?s result [3], prove that S-resolvent norm bounded is not constant any open set set. Beside, find characterization S-pseudospectrum operator means S-spectra all perturbed with perturbations have norms strictly less than ?.