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 compactness of strongly continuous semigroups and cosine functions of operators

Author: Hernán R. Henríquez
Journal: Proc. Amer. Math. Soc. 123 (1995), 1417-1424
MSC: Primary 47D03; Secondary 47B07, 47D09
MathSciNet review: 1227517
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we relate two notions of compactness for strongly continuous semigroups of linear operators and cosine functions of linear operators. Specifically, if T denotes a strongly continuous semigroup of linear operators defined on a Banach space X, we will show that T is compact if and only if the set $ \{ (T( \bullet )x:x \in X,\left\Vert x \right\Vert \leq 1\} $ is relatively compact in any space $ {L^p}([0,a]);X)$ for $ 1 \leq p < \infty $ and $ a > 0$. We establish similar results for $ {(T(t) - I)^n},n \in {\mathbf{N}}$, and for cosine and sine functions of operators.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47D03, 47B07, 47D09

Retrieve articles in all journals with MSC: 47D03, 47B07, 47D09

Additional Information

PII: S 0002-9939(1995)1227517-2
Keywords: Semigroup of operators, cosine functions of operators, compact operators
Article copyright: © Copyright 1995 American Mathematical Society

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