Spectral theory of (n, m)-normal operators on Hilbert space

Abstract

In this work, we define the set which consists of (n, m)-normal operators. Also, the sets and and defined from . Firstly, the set is proved Banach algebra and establish consists of (n, m)-normal operators. Secondly, we give theorem of the Gelfand representation of the Banach algebra generated by a (n, m)-normal operator, also some theories are proven to reach a circular for the spectral theory. Finally, this study is established and proved generalization the spectral theory of (n, m)-normal operators.