Operators with absolute continuity properties: an application to quasinormality
Volume 215 / 2013
Studia Mathematica 215 (2013), 11-30
MSC: Primary 47B20; Secondary 47B37.
DOI: 10.4064/sm215-1-2
Abstract
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of $q$-quasinormal operators are established.
