Operators with absolute continuity properties: an application to quasinormality

被引：5
|
作者：
Jablonski, Zenon Jan [1 ]
Jung, Il Bong [2 ]
Stochel, Jan [1 ]
机构：
[1] Uniwersytet Jagiellonski, Inst Matemat, PL-30348 Krakow, Poland
[2] Kyungpook Natl Univ, Dept Math, Taegu 702701, South Korea
来源：
STUDIA MATHEMATICA | 2013年 / 215卷 / 01期
基金：
新加坡国家研究基金会;
关键词：
quasinormal operator; spectral measure; absolute continuity; weighted shift on a directed tree; q-quasinormal operator; NORMAL EXTENSIONS; SUBNORMALITY; THEOREM;
D O I：
10.4064/sm215-1-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：11 / 30
页数：20
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