Spectrum of bounded operators in Hilbert spaces

This paper makes an attempt to study the spectrum operators by emphasising on condition of commuting operators so as to expose more properties in the classes of operators. Here, study of various classes of bounded operators on a Hilbert space H is one of the most important topics in the preparation of the study of the Hilbert spaces. In case a abounded operator A commutes at least with its own adjoint A* it forms important classes of operators on H, eg normal, unitary, self–adjoint etc. The operators under the study are bounded operators operating in a complete space called Hilbert spaces.