Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41420150801Analytic extension of a $N$th roots of $M$-hyponormal operator945954664ENJ.ShenSchool of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, ChinaA.ChenDepartment of Mathematics, Hohhot Minzu College, 010051, Hohhot, China, and,
School of Mathematical Sciences, Inner Mongolia University, 010021, Hohhot, ChinaJournal Article20130922In 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 $2kn+2$.http://bims.iranjournals.ir/article_664_cbd29cea015607395ebabc120fa75053.pdf