Remarks on spectral properties of $p$-hyponormal and log-hyponormal operators
Bull. Korean Math. Soc. 2005 Vol. 42, No. 3, 543-554
Printed September 1, 2005
Bhagwati P. Duggal and In Ho Jeon
Ewha Women's University
Abstract : 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
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