ABSTRACT
This chapter is devoted to functions of noncompact nonself adjoint operators, and lists some well-known notions of the theory of linear operators in a Hilbert space. It deals with the so called triangular representation of linear operators. This representation is the basis for obtaining the norm estimations. The chapter analyzes general operators admitting the triangular representation, and considers the resolvent of a quasiunitary operator, that is, an operator which is a sum of a unitary and a compact operator. It is concerned with regular functions of operators admitting the triangular representation. A multiplicative representation for a resolvent of a nonselfadjoint operators is derived. The chapter establishes a norm estimation for the resolvent of operators admitting the triangular representation.
