Some spectral mapping theorems through local spectral theory

被引：1

作者：

Aiena P. ^{[1
]}

Biondi M.T. ^{[2
]}

机构：

[1] Dipartimento di Matematica ed Applicazioni Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Viale delle Scienze

[2] Departmento de Matemáticas, Facultad de Ciencias, Universidad UCLA de Barquisimeto

来源：

Rendiconti del Circolo Matematico di Palermo | 2004年 / 53卷 / 2期

关键词：

Single valued extension property; spectral mapping theorems; Weyl and semi-Browder operators; Weyl's theorem;

D O I：

10.1007/BF02872869

中图分类号：

学科分类号：

摘要：

The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that if T or T* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the case T or T* has the single valued extension property, to f(T), where f is an analytic function defined on an open disc containing the spectrum of T. In the last part we improve a recent result of Curto and Han [10] by proving that for every transaloid operator T a-Weyl's theorem holds for f(T) and f(T)*. © 2004 Springer.

引用

页码：165 / 184

页数：19

共 36 条

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[2] Aiena P., Monsalve O., The single valued extension property and the generalized Kato decomposition property, Acta Sci. Math. (Szeged), 67, pp. 461-477, (2001)
[3] Aiena P., Carpintero C., Single valued extension property and semi-Browder spectra, To appear in Acta Sci. Math. (Szeged), (2003)
[4] Aiena P., Carpintero C., Weyl's theorem, a-Weyl's theorem and single-valued extension property, (2003)
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[6] Aiena P., Miller T.L., Neumann M.M., On a localized single valued extension property, To appear on Proc. of Roy. Irish Acad., (2002)
[7] Aiena P., Rosas E., The single valued extension property at the points of the approximate point spectrum, J. Math. Anal. Appl., 279, 1, pp. 180-188, (2003)
[8] Aiena P., Mbekhta M., Characterization of some classes of operators by means of the Kato decomposition, Boll. Un. Mat. It., 10 A, pp. 609-621, (1996)
[9] Caradus S.R., Pfaffenberger W.E., Yood B., Calkin Algebras of Operators and Algebras of Operators on Banach Spaces, (1974)
[10] Curto R.E., Han Y.M., Weyl's theorem, a-Weyl's theorem, and local spectral theory, J. London Math. Soc., 67, 2, pp. 499-509, (2003)

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