| A NOTE ON REDUCTIVITY OF OPERATORS |
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| 引用本文： | Liu Longfu. A NOTE ON REDUCTIVITY OF OPERATORS[J]. 数学年刊B辑(英文版), 1983, 4(2): 191-192 |
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| 作者姓名： | Liu Longfu |
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| 作者单位： | Jilin University |
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| 摘 要： | P. Rosenthal introduced the following property(P):If u is any reductive algebra and T∈u', then T~*∈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 polynomially compact operator, then T is normal.
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| 修稿时间： | 1982-10-04 |
A NOTE ON REDUCTIVITY OF OPERATORS |
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| Liu Longfu. A NOTE ON REDUCTIVITY OF OPERATORS[J]. Chinese Annals of Mathematics,Series B, 1983, 4(2): 191-192 |
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| Authors: | Liu Longfu |
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| Affiliation: | Jilin University |
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| 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 Tis normal. |
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