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)

 

On the perturbation theory
of $m$-accretive operators
in Banach spaces


Author: Athanassios G. Kartsatos
Journal: Proc. Amer. Math. Soc. 124 (1996), 1811-1820
MSC (1991): Primary 47H17; Secondary 47B44, 47H09, 47H10
MathSciNet review: 1327021
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $X$ be a real Banach space. Let $T:X\supset D(T)\to 2^{X}$ be $m$-accretive with $(T+I)^{-1}$ compact. Let $C:X\supset D(T)\to X$ be such that $C(I+\lambda T)^{-1}:X\to X$ is condensing for some $\lambda \in (0,1).$ Let $p\in X$ and assume that there exists a bounded open set $G\subset X$ and $z\in D(T)\cap G$ such that $C(D(T)\cap \overline G)$ is bounded and

\begin{equation*}\langle u+Cx-p,j\rangle \ge 0,\tag *{(*)}\end{equation*}

for all $x\in D(T)\cap \partial G,~u\in Tx,~j\in J(x-z).$ Then $p\in (T+C)(D(T)\cap \overline G).$ A basic homotopy result of the degree theory for $I-A,$ with $A$ condensing and $D(A)$ possibly unbounded, is used to improve and/or extend recent results by Hirano and Kalinde.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47H17, 47B44, 47H09, 47H10

Retrieve articles in all journals with MSC (1991): 47H17, 47B44, 47H09, 47H10


Additional Information

Athanassios G. Kartsatos
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: hermes@gauss.math.usf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03349-7
PII: S 0002-9939(96)03349-7
Keywords: Accretive operator, $m$-accretive operator, compact perturbation, compact resolvent, degree theory for condensing mappings
Received by editor(s): December 5, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society