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| On the Spectra!Subspaces of the Non-Normal Operators |
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Citation： |
Li Shaokuan.On the Spectra!Subspaces of the Non-Normal Operators[J].Chinese Annals of Mathematics B,1982,3(3):303~308 |
| Page view： 773
Net amount： 886 |
Authors： |
Li Shaokuan; |
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| Abstract： |
In this paper we have proved
Theorem 2. Let T be an operator on the Hilbert space II with the single valued extension property, Suppose that for every X in the complex plane, it holds that
$||(T-\lambda)f||^2 \leq ||(T-\lambda)^2f||\cdot ||f||,\forall f \in H$
Then for any closed subset \delta of the plane, the spectral subspace ￡_T (\delta) is closed.
Theorem 9. Let T and S^* be semi-hyponormal operators and 0 \notin \sigma_p(s). Suppose that there exists an injective operator W with dense range which satisfies
TW = WS.
Then T and S are normal operators.
Theorem 10. Let S be a co-semi-hyponormal operator with the single valued extension property and be not normal. Then there exists f \ne 0 which satisfies
${\sigma _s}(f) \not\subset \sigma (S)$ |
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