Spectral Theory For a Class Of Non-Normal Operators

Abstract

1. Introduction. As is well known, the spectral theorem plays an important part in mathematics because of its many applications. Unfortunately, the theorem is valid for normal operators only. In view of this, attempts have been made by several mathematicians to obtain a theorem about a more general class of operators, which will reduce to the ordinary spectral theorem if the operator is normal. Brown (1) has developed a unitary equivalence theory for a certain class of operators.