%0 Journal Article
%T Analytic extension of a $N$th roots of $M$-hyponormal operator
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Shen, J.
%A Chen, A.
%D 2015
%\ 08/01/2015
%V 41
%N 4
%P 945-954
%! Analytic extension of a $N$th roots of $M$-hyponormal operator
%K $n$th roots of $M$-hyponormal operator
%K Bishop's property ($\beta$)
%K subscalar operator
%K invariant subspace
%R
%X 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 $2kn+2$.
%U http://bims.iranjournals.ir/article_664_cbd29cea015607395ebabc120fa75053.pdf