Abstract. This article deals with operators that are $p$-hyponormal for every $p>0$ under the name of $\infty $-hyponormal operators. A characterization of such operators is given, and their properties are investigated. Special attention is paid to the spectral property of $\infty $-hyponormal operators having dense ranges and no non-trivial reducing subspaces.
AMS Subject Classification
(1991): 47B20, 47A63
Keyword(s):
p,
-hyponormal operator,
spectral resolution,
polar decomposition,
spectrum,
\infty,
-hyponormal operator
Received March 1, 2000, and in revised form September 12, 2000. (Registered under 2788/2009.)
|