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Abstract. Characterizations of the classes of $p$-hyponormal, $\infty $-hyponormal and weak hyponormal weighted composition operators are shown. It is shown that some classes of weak hyponormal weighted composition operators can not be separated. It is an extension of the result by C. Burnap, etc.
AMS Subject Classification
(1991): 47B33, 47B20
Keyword(s):
weighted composition operators,
$p$-hyponormal operators,
class A($p,
r$) operators,
absolute-$(p,
r)$-paranormal operators,
$p$-quasihyponormal operators,
conditional expectation
Received August 5, 2008, and in final form December 1, 2009. (Registered under 60/2010.)
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