Liu Longfu.A NOTE ON REDUCTIVITY OF OPERATORS[J].Chinese Annals of Mathematics B,1983,4(2):191~192
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Authors：
Liu Longfu;
Abstract：
P. Rosenthal introduced the following property (P):
If U is any reductive algebra and $\[T \in U\]$, then $\[{T^*} \in {U^'}\]$.
In this note, the author proves
(1)A reductive spectral operator with polynomially compact quasinilpotent part has property (P);
(2)A reductive spectral operator with algebraic quasinilpotent part has property (P);
(3)The countable direct sum of scalar operators has property (P);
(4)If T is reductive and T is quasi-similar to a palynomially compact operator, then T
is normal.
