Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

An Atkinson-type theorem for B-Fredholm operators

100%

Berkani M., Sarih M.

Studia Mathematica

2001

tom 148

nr 3

251-257

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].

Ograniczanie wyników

1 Studia Mathematica

1 Berkani M.

1 Sarih M.

1 2001

Wyniki wyszukiwania

An Atkinson-type theorem for B-Fredholm operators