Geodesic
Operators with absolute continuity properties: an application to quasinormality
Zenon Jan Jabłoński1 ; Il Bong Jung2 ; Jan Stochel1
1Instytut Matematyki Uniwersytet Jagielloński Łojasiewicza 6 30-348 Kraków, Poland
2Department of Mathematics Kyungpook National University Daegu 702-701, Korea
Studia Mathematica, Tome 215 (2013) no. 1, pp. 11-30
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm215-1-2
Keywords: absolute continuity approach quasinormality which relates operator question spectral measure its modulus developed algebraic characterizations classes operators emerge context found various examples counterexamples illustrating concepts paper constructed using weighted shifts directed trees generalizations these results cover q quasinormal operators established

Zenon Jan Jabłoński  1   ; Il Bong Jung  2   ; Jan Stochel  1

1 Instytut Matematyki Uniwersytet Jagielloński Łojasiewicza 6 30-348 Kraków, Poland
2 Department of Mathematics Kyungpook National University Daegu 702-701, Korea 
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 an application to quasinormality},
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Zenon Jan Jabłoński; Il Bong Jung; Jan Stochel. Operators with absolute continuity properties:
 an application to quasinormality. Studia Mathematica, Tome 215 (2013) no. 1, pp. 11-30. doi: 10.4064/sm215-1-2

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