# ON WEIGHTED WEYL SPECTRUM, II

• 발행 : 2006.11.30

#### 초록

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

#### 참고문헌

1. S. C. Arora and P. Arora, On operators satisfying Re $\sigma_{\alpha}$(T) = $\sigma_{\alpha}$(Re T), J. Indian Math. Soc. 48 (1984), no. 1-4, 201-204
2. S. R. Caradus, W. E. Pfaffenberger, and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Marcel Dekker, New York, 1974
3. J. B. Conway, Subnormal operators, Pitman, Boston, 1981
4. P. Dharmarha, Weighted Weyl spectrum, Preprint
5. G. Edgar, J. Ernest, and S. G. Lee, Weighing operator spectra, Indiana Univ. Math. J. 21 (1971), no. 1, 61-80 https://doi.org/10.1512/iumj.1971.21.21005
6. W. Y. Lee and S. H. Lee, A spectral mapping theorem for the Weyl spectrum, Glasgow Math. J. 38 (1996), no. 1, 61-64 https://doi.org/10.1017/S0017089500031268
7. J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176 https://doi.org/10.1215/S0012-7094-51-01813-3
8. K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212
9. S. K. Berberian, Conditions on an operator implying Re $\sigma_{\alpha}$(T) = $\sigma_{\alpha}$(Re T), Trans. Amer. Math. Soc. 154 (1971), 267-272 https://doi.org/10.2307/1995442

#### 피인용 문헌

1. On <i>α</i>-Weyl Operators vol.06, pp.03, 2016, https://doi.org/10.4236/apm.2016.63011