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J. Korean Math. Soc. 2016; 53(1): 233-246
Printed January 1, 2016
https://doi.org/10.4134/JKMS.2016.53.1.233
Copyright © The Korean Mathematical Society.
Analytic extensions of $M$-hyponormal operators
Salah Mecheri and Fei Zuo
Taibah University, Henan Normal University
In this paper, we introduce the class of analytic extensions of $M$-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an $M$-hyponormal operator $T$ is subscalar of order $2k+2$. Finally we obtain that an analytic extension of an $M$-hyponormal operator satisfies Weyl's theorem.
Keywords: $M$-hyponormal operator, Bishop's property ($\beta$), subscalar operator, Weyl's theorem
MSC numbers: Primary 47B20, 47A15
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