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

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Continuous dependence of solutions of operator equations. I

Author: Zvi Artstein
Journal: Trans. Amer. Math. Soc. 231 (1977), 143-166
MSC: Primary 47H15
MathSciNet review: 0445351
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Continuous dependence of the solutions of the operator equation $ x = Tx + z$ in a topological vector space is the main subject of the paper. We find sufficient and necessary conditions for the continuous dependence on the data (T, z) or on a parameter. We do it for the space of all closed operators. Equivalent conditions for particular subfamilies are discussed. Among other families we deal with compact operators, compact perturbations of the identity, condensing operators and demicompact operators.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47H15

Retrieve articles in all journals with MSC: 47H15

Additional Information

PII: S 0002-9947(1977)0445351-1
Keywords: Continuous dependence on parameters, closed operators, compact operators, condensing operators, fixed points, ODE, FDE
Article copyright: © Copyright 1977 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