M.Sc. Tezi Görüntüleme

      In this study the spectrum of some normal operators and hyponormal operators are investigated in terms of the spectrum of their reel and imaginary parts in Hilbert space.

      In the second part firstly, the point spectrum of a normal operator is stated with a special Cartesian product in terms of the point spectrum of its real and imaginary parts. Therefore, when its real and imaginary parts are compact operators, the conditions in which its point spectrum is expressed with normal Cartesian product in terms of the point spectrum of its real and imaginary parts are investigated. Also the same study is made for hyponormal operators. After that the structure of a normal operator spectrum is studied carefully and conditions in which its spectrum is expressed with Cartesian product in terms of the point spectrum of its real and imaginary parts are given. Finally, applications of spectral radius, numerical radius, its norm for bounded normal operators and asymptotical behaviour of the eigenvalues for unbounded normal operators are given with all results. Moreover, all theorems in this thesis are supported with examples.

      Keywords: Normal Hyponormal Operator and Unitary Operators; Function of an Operator; Spectrum and Rezolvent

       Modules of Eigenvalues.