Bull. Korean Math. Soc. 2005 Vol. 42, No. 3, 571-577 Printed September 1, 2005

Bhagwati P. Duggal, In Ho Jeon, and Eungil Ko

Abstract : In this paper we prove that if $T$ is a $k$-th root of a $p$-hyponormal operator when $T$ is compact or $T^n$ is normal for some integer $n>k$, then $T$ is (generalized) scalar, and that if $T$ is a $k$-th root of a semi-hyponormal operator and have the property $\sigma(T)$ is contained in an angle $< \frac{2\pi}{k}$ with vertex in the origin, then $T$ is subscalar.

Keywords : $k$-th roots of $p$-hyponormal operator, subscalar operator