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 $2kn+2$.
Shen, J., & Chen, A. (2015). Analytic extension of a $N$th roots of $M$-hyponormal operator. Bulletin of the Iranian Mathematical Society, 41(4), 945-954.
MLA
Shen, J., & Chen, A. "Analytic extension of a $N$th roots of $M$-hyponormal operator", Bulletin of the Iranian Mathematical Society, 41, 4, 2015, 945-954.
HARVARD
Shen J., Chen A. (2015). 'Analytic extension of a $N$th roots of $M$-hyponormal operator', Bulletin of the Iranian Mathematical Society, 41(4), pp. 945-954.
CHICAGO
J. Shen & A. Chen, "Analytic extension of a $N$th roots of $M$-hyponormal operator," Bulletin of the Iranian Mathematical Society, 41 4 (2015): 945-954,
VANCOUVER
Shen J., Chen A. Analytic extension of a $N$th roots of $M$-hyponormal operator. BIMS. 2015;41(4):945-954.
