Abstract. Given a $p$-hyponormal operator $(0< p< 1/2)$ $T$ on a Hilbert space, define operators $\hat T$ and $\tilde T$ by $\hat T=| T| ^{1/2}U| T| ^{1/2}$ and $\tilde T=| \hat T| ^{1/2}V| \hat T| ^{1/2}$, where the partial isometries $U$ and $V$ are as in the polar decompositions $T=U| T| $ and $\hat T=V| \hat T| $. The operator $\tilde T$ is then hyponormal. We show that $T$ has a non-trivial invariant subspace if and only if $\tilde T$ does, and that if $T$ does not have a non-trivial invariant subspace, then $T$ is the compact perturbation of a normal operator. We also consider upper triangular operators with $p$-hyponormal entries along the main diagonal.
AMS Subject Classification
(1991): 47A15, 47B20
Keyword(s):
p,
-hyponormal operator,
invariant subspace,
compact perturbation
Received May 6, 1997. (Registered under 2660/2009.)
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