On the perturbation theory of <IMG ALIGN=BOTTOM >-accretive operators in Banach spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the perturbation theory of -accretive operators in Banach spaces

Authors:	Athanassios G Kartsatos

Institution:	Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700

Abstract:	Let be a real Banach space. Let $T:X\supset D(T)\to 2^{X}$ be -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 with condensing and possibly unbounded, is used to improve and/or extend recent results by Hirano and Kalinde.

Keywords:	Accretive operator $m$-accretive operator compact perturbation compact resolvent degree theory for condensing mappings

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