An Atkinson-type theorem for B-Fredholm operators

• Autorzy: M. Berkani , M. Sarih
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space and let T be a bounded linear operator acting on X. Atkinson's well known theorem says that T is a Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is invertible, where F₀(X) is the ideal of finite rank operators in the algebra L(X) of bounded linear operators acting on X. In the main result of this paper we establish an Atkinson-type theorem for B-Fredholm operators. More precisely we prove that T is a B-Fredholm operator if and only if its projection in the algebra L(X)/F₀(X) is Drazin invertible. We also show that the set of Drazin invertible elements in an algebra A with a unit is a regularity in the sense defined by Kordula and Müller [8].

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 16U99: None of the above, but in this section
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 148
• Numer: 3
• Strony: 251-257

Daty

wydano

2001

Twórcy

autor

M. Berkani

• Département de Mathématiques, Faculté des Sciences, Université Mohammed I, Oujda, Maroc

autor

M. Sarih

• Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, Kénitra, Maroc

Identyfikatory

DOI

10.4064/sm148-3-4