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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
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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.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-96-03349-7
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