B-fredholm and spectral properties for multipliers in Banach algebras

被引：5

作者：

Berkani M. ^{[1
]}

Arroud A. ^{[1
]}

机构：

[1] Département de Mathématiques, Groupe d'Analyse et Théorie des Opérateurs (G.A.T.O), Université Mohammed I, Faculté des Sciences, Oujda

来源：

Rendiconti del Circolo Matematico di Palermo | 2006年 / 55卷 / 3期

关键词：

B-Fredholm operators; Banach Algebras; generalized Weyl's theorem; Multipliers; Weyl's theorem;

D O I：

10.1007/BF02874778

中图分类号：

学科分类号：

摘要：

The main purpose of this paper is to study spectral and B-Fredholm properties of a multiplier T acting on a semi-simple regular tauberian commutative Banach algebra A. We show that T is a B-Fredholm operator if and only if T is a semi B-Fredholm operator, and in this case we have the index ind(T)=0. Moreover we give some spectral properties for multipliers. Spectral mapping theorems for the Weyl's and B-Weyl spectrum of a multiplier are also considered. Furthermore we show that Weyl's theorem and generalized Weyl's theorem hold for a multiplier T. Finally we give sufficient conditions for a multiplier to be a product of an invertible and an idempotent operators. © 2006 Springer.

引用

页码：385 / 397

页数：12

共 23 条

[1]

Aiena P., The Weyl-Browder spectrum of a multiplier, Contemporary Mathematics, 232, pp. 13-21, (1999)

[2]

Aiena P., Fredholm and local spectral theory, with application to multipliers, (2004)

[3]

Aiena P., Villafane F., Weyl's theorem for some classes of operators, Integral Eequations and Operator Theory, 53, pp. 453-466, (2005)

[4]

Aiena P., Laursen K.B., Multipliers with closed range on regular commutative banach algebras, Proc. Am. Math. Soc., 121, pp. 1039-1048, (1994)

[5]

Berkani M., On a class of quasi-Fredholm operators, Integr. Equ. Oper. Theory, 34, pp. 244-249, (1999)

[6]

Berkani M., Sarih M., On semi B-Fredholm operators, Glasg. Math. J., 43, pp. 457-465, (2001)

[7]

Berkani M., Sarih M., An Atkinson-type theorem for B-Fredholm operators, Studia Math., 148, pp. 251-257, (2001)

[8]

Berkani M., Index of B-Fredholm operators and Generalization of a Weyl Theorem, Proc. Amer. Math. Soc., 130, pp. 1717-1723, (2002)

[9]

Berkani M., B-Weyl spectrum and poles of the resolvent, J. Math. Anal. Applications, 272, pp. 596-603, (2002)

[10]

Berkani M., Koliha J.J., Weyl type theorems for bounded linear operators, Acta Sci. Math. (Szeged), 69, pp. 359-376, (2003)

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