Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

An Atkinson-type theorem for B-Fredholm operators

Tom 148 / 2001

Studia Mathematica 148 (2001), 251-257 MSC: 16U99, 47A10, 47A53. DOI: 10.4064/sm148-3-4

Streszczenie

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 $L(X)/ F_{0}(X)$ is invertible, where $F_{0}(X)$ 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 $L(X)/ F_{0}(X)$ 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].

Autorzy

• M. BerkaniDépartement de Mathématiques
Faculté des Sciences
Université Mohammed I
Oujda, Maroc
e-mail
• M. SarihDépartement de Mathématiques
Faculté des Sciences
Université Ibn Tofail
Kénitra, Maroc

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek