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A Leray–Schauder type theorem for approximable maps in topological vector spaces

✍ Scribed by In-Sook Kim

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
475 KB
Volume
47
Category
Article
ISSN
0362-546X

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✦ Synopsis

We give new Leray-Schauder type theorems for compact or condensing approximable maps in not necessarily locally convex topological vector spaces in two different ways of approach. First, with the help of the (Z) type set, our argument is based on a finite dimensional approximation property for topological vector spaces without appeal to topological degree and the homotopy extension theorem. Secondly, using a fixed point theorem on admissible topological vector spaces in the sense of Klee, we present simple proofs of the Leray-Schauder type theorems for compact or condensing approximable maps.

📜 SIMILAR VOLUMES

Leray-Schauder alternatives for approxim
Leray-Schauder alternatives for approximable maps in topological vector spaces
✍ In-Sook Kim; Kihong Kim; Sehie Park 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 564 KB

using a fixed-point theorem for compact approximable maps defined on an admisssible convex subset of a topological vector space, we prove Leray-Schauder alternatives for compact or pseudo-condensing approximable maps.