On spectra of n-hyponormal operators in Hilbert space

Abstract

Many practical applications of Mathematics rely on results in operator theory. In this paper we focus on the characterization of the spectrum of a hyponormal operator and the spectrum of its adjoint. Considering an atomic quantum mechanical system, if A is an operator of an atom, then the differences of the various eigenvalues of A are the amounts of energy emitted by the atom as it undergoes transitions. These amounts are seen in the form of electromagnetic waves, which constitute the optical spectrum of the report. The main objective will be finding a formal evaluation of the spectra of hyponormals and the spectrum of its adjoint. Emphasis will also be on the resultant spectra of similar operators to find any relationships.