AC(sigma) OPERATORS

作者：Ashton Brenden^*; Doust Ian

来源：Journal of Operator Theory, 2011, 65(2): 255-279.

• Functions of bounded variation
• absolutely continuous functions
• functional calculus
• AC-operators
• well-bounded operators

In this paper we present a new extension of the theory of well-bounded operators to cover operators with complex spectrum. In previous work a new concept of the class of absolutely continuous functions on a nonempty compact subset sigma of the plane, denoted AC(sigma), was introduced. An AC(sigma) operator is one which admits a functional calculus for this algebra of functions. The class of AC (sigma) operators includes all of the well-bounded operators and trigonometrically well-bounded operators, as well as all scalar-type spectral operators, but is strictly smaller than Berkson and Gillespie's class of AC operators. This paper develops the spectral properties of AC (sigma) operators and surveys some of the problems which remain in extending results from the theory of well-bounded operators.

• 出版日期2011