On quasi-$A(n,k)$ class operators
Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 741-750
https://doi.org/10.4134/CKMS.2013.28.4.741
Printed October 1, 2013
Mi Ryeong Lee and Hye Yeong Yun
Kyungpook National University, Kyungpook National University
Abstract : To study the operator inequalities, the notions of class $A$ operators and quasi-class $A$ operators are developed up to recently. In this paper, quasi-$A(n,k)$ class operator for $n\geq 2$ and $k\geq 0$ is introduced as a new notion, which generalizes the quasi-class $A$ operator. We obtain some structural properties of these operators. Also we characterize quasi-$A(n,k)$ classes for $n$ and $k$ via backward extension of weighted shift operators. Finally, we give a simple example of quasi-$A(n,k)$ operators with two variables.
Keywords : class $A$, quasi-class $A$, weighted shift operator
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