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).

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