Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The asymptotic behaviour of the reduced minimum modulus of a Fredholm operator


Authors: K.-H. Förster and M. A. Kaashoek
Journal: Proc. Amer. Math. Soc. 49 (1975), 123-131
MSC: Primary 47A55; Secondary 47B30
MathSciNet review: 0372660
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \gamma (S)$ denote the reduced minimum modulus of a linear operator $ S$ acting in a complex Banach space $ X$, and let $ I$ denote the identity on $ X$. In this paper it is shown that for a (not necessarily bounded) Fredholm operator $ T$ acting in $ X$, the limit $ {\lim _{n \to \infty }}\gamma {({T^n})^{1/n}}$ exists and is equal to the supremum of all positive numbers $ \delta $ such that the dimension of the null space and the codimension of the range of $ T - \lambda I$ are constant on $ 0 < \vert\lambda \vert < \delta $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A55, 47B30

Retrieve articles in all journals with MSC: 47A55, 47B30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0372660-0
PII: S 0002-9939(1975)0372660-0
Keywords: Fredholm and semi-Fredholm operators, reduced minimum modulus, stability theory, spectrum
Article copyright: © Copyright 1975 American Mathematical Society