S-essential spectra and the Weyl pseudospectra of linear operators

In this work we present a spectral study of semi regular operator. The concept of semi regularity and essentially semi regularity amongst the various concepts of regularity originating from Fredholm theory, and we introduce new notions and unprecedented denition to develop pseudospectral theory. We built our denition on the basis of essential spectra and tried to comply it with pseudospectral theory. So, we intend to obtain what we call "Weyl pseudospectra".