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

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- by Athanassios G. Kartsatos
- Proc. Amer. Math. Soc.
**124**(1996), 1811-1820 - DOI: https://doi.org/10.1090/S0002-9939-96-03349-7
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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.## References

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## Bibliographic Information

**Athanassios G. Kartsatos**- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- Email: hermes@gauss.math.usf.edu
- Received by editor(s): December 5, 1994
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**124**(1996), 1811-1820 - MSC (1991): Primary 47H17; Secondary 47B44, 47H09, 47H10
- DOI: https://doi.org/10.1090/S0002-9939-96-03349-7
- MathSciNet review: 1327021