Abstract. It is known that any positive integer power of an $\omega $-hyponormal operator is $\omega $-hyponormal. In this note we show that, for any $0< p\leq1$, there exists an invertible operator whose integer powers are all $p-\omega $-hyponormal. We also show that there exists a ${1\over2}-\omega $-hyponormal operator $T$ such that $T^3$ is not ${1\over2}-\omega $-hyponormal.
AMS Subject Classification
(1991): 47B20, 47A63
Keyword(s):
p-$\omega$,
$\omega$-hyponormal,
Furuta inequality
Received June 26, 2003. (Registered under 5874/2009.)
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