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The Lefschetz type theorem for a class of noncompact mappings. (English) Zbl 0641.55002
Abstract analysis, Proc. 14th Winter Sch., SrnĂ®/Czech. 1986, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 14, 365-384 (1987).
[For the entire collection see Zbl 0627.00012.]
The author develops a concept of trace for mappings on vector spaces that are compatible with a filtration. Using this concept he defines a generalized Lefschetz number and applies this to uniform Hausdorff spaces with a filtration and corresponding (“admissible”) maps. Under certain natural assumptions the generalized Lefschetz number for such mappings will exist, and a nonvanishing Lefschetz number will give rise to an approximate fixed point. The details are highly laborious and too technical to be explained here.
Reviewer: Ch.Fenske

MSC:
55M25 Degree, winding number
47H10 Fixed-point theorems
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