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


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


Zbl 0627.00012
Full Text: EuDML