Bulletin of the
Korean Mathematical Society BKMS

In this paper it is proved that for $p$-hyponormal or log-hyponormal operator $A$ there exist an associated hyponormal operator $T$, a quasi-affinity $X$ and an injection operator $Y$ such that $TX=XA$ and $AY=YT$.~The operator $A$ and $T$ have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of $p$-hyponormal and log-hyponormal operators, amongst them that the spectrum is a continuous function on these classes of operators.

Keywords: $p$-hyponormal operator, log-hyponormal operator, spectral picture

MSC numbers: 47B20, 47A10