Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the poles of the resolvent in Calkin algebra

Author: O. Bel Hadj Fredj
Journal: Proc. Amer. Math. Soc. 135 (2007), 2229-2234
MSC (2000): Primary 47L10
Published electronically: March 2, 2007
MathSciNet review: 2299500
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the present note, we study the problem of lifting poles in Calkin algebra on a separable infinite-dimensional complex Hilbert space $ H$. We show by an example that such lifting is not possible in general, and we prove that if zero is a pole of the resolvent of the image of an operator $ T$ in the Calkin algebra, then there exists a compact operator $ K$ for which zero is a pole of $ T+K$ if and only if the index of $ T-\lambda$ is zero on a punctured neighbourhood of zero. Further, a useful characterization of poles in Calkin algebra in terms of essential ascent and descent is provided.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47L10

Retrieve articles in all journals with MSC (2000): 47L10

Additional Information

O. Bel Hadj Fredj
Affiliation: Université Lille 1, UFR de Mathématiques, UMR-CNRS 8524, 59655 Villeneuve d’Ascq, France

PII: S 0002-9939(07)08733-3
Keywords: Poles, Calkin algebra, essential ascent and essential descent
Received by editor(s): February 6, 2006
Received by editor(s) in revised form: March 28, 2006
Published electronically: March 2, 2007
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia