CHARACTERIZATION OF OPERATORS OF CLASS G1,SPECTRAL G1, CLASS LOC-G1 AND SPECTRAL LOC-G1 IN A HILBERT SPACE

Abstract

A normal operator has been an object of much study in operator theory and possesses many nice properties and non-normal operators can be classified according to their satisfying some of such properties or generalization of some of these properties. According, sufficient conditions for a bounded operator T to be of class G1, spectral G1 – class, class loc –G1 and some properties of class R are discussed.