Analytic extension of a $N$th roots of $M$-hyponormal operator

Shen, J.; Chen, A.

Analytic extension of a $N$th roots of $M$-hyponormal operator

Document Type : Research Paper

Authors

J. Shen ¹
A. Chen ²

¹ School of Mathematical Sciences‎, ‎Inner Mongolia University‎, ‎010021‎, ‎Hohhot‎, ‎China

² Department of Mathematics‎, ‎Hohhot Minzu College‎, ‎010051‎, ‎Hohhot‎, ‎China, and, ‎School of Mathematical Sciences‎, ‎Inner Mongolia University‎, ‎010021‎, ‎Hohhot‎, ‎China

Abstract

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $\mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎we show that the sum of a $n$th roots of $M$-hyponormal operator and an algebraic operator of order $k$ which are commuting is subscalar of order $2kn+2$‎.

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