A note on the index of B-Fredholm operators

Title:

A note on the index of B-Fredholm operators

Creator:

Berkani, M. and Medková, Dagmar

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c3c4f86d-0ec6-418a-be4b-16487bd5f039
uuid:c3c4f86d-0ec6-418a-be4b-16487bd5f039

Subject:

B-Fredholm operators and index of the product of Fredholm operators

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251– 257] we know that if S, T are commuting B-Fredholm operators acting on a Banach space X, then ST is a B-Fredholm operator. In this note we show that in general we do not have ind(ST) = ind(S) + ind(T), contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist U, V ∈ L(X) such that S, T, U, V are commuting and US + V T = I, then ind(ST) = ind(S) + ind(T), where ind stands for the index of a B-Fredholm operator.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

177-180

Source:

Mathematica bohemica | 2004 Volume:129 | Number:2

Harvested from:

CDK

Metadata only:

false