Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on March 12, 2008
Proceedings of the London Mathematical Society 2008 97(1):97-116; doi:10.1112/plms/pdm058
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
97/1/97    most recent
pdm058v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Dungey, N.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

On time regularity and related conditions for power-bounded operators

Nick Dungey

Department of Mathematics
Macquarie University
NSW 2109
Australia

Received 2 April 2007. Revision received 14 November 2007.

Let T be a bounded linear operator in a complex Banach space. Our main result gives various characterizations of the condition: T is power-bounded and an estimate ||(I – T)Tn || ≤ cn– 1/2 holds for all positive integers n. In particular, this condition holds if and only if T = β S + (1 – β)I, for some β isin (0, 1) and some power-bounded operator S; or if and only if T is power-bounded and the discrete semigroup (Tn) is dominated by the continuous semigroup (e– t(I – T))t ≥ 0 in a natural sense. As a consequence of our main results, for 1/2 < {alpha} ≤ 1 we characterize the condition that T is power-bounded and ||(I – T)Tn || ≤c n– {alpha} for all n, in terms of estimates on the semigroup e–t(I – T).

2000 Mathematics Subject Classification 47A30, 47A10 (primary), 47D06 (secondary).


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.