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Journal of Operator Theory

Volume 48, Issue 1, Summer 2002  pp. 151-186.

Some classes of $q$-deformed operators

Authors:  Schoichi Ota
Author institution: Department of Mathematics, Kyushu Institute of Design, Fukuoka, 815-8540, Japan

Summary:  Motivated by recent developments in the theory of quantum groups, some classes of $q$-deformed operators ($q$-normal, $q$-quasinormal, $q$-hyponormal operators) are introduced and investigated systematically, where $q$ is a positive deformation parameter. It turns out that many basic properties of these $q$-deformed operators are different from that of the corresponding undeformed operators (i.e., normal, quasinormal, hyponormal operators).

Keywords:  Unbounded operator, quantum group, $q$-normal operator, $q$-deformed operator, weighted shift, powers of operators

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