The Lefschetz type theorem for a class of noncompact mappings. (English) Zbl 0641.55002

Kryszewski, W.

Abstract analysis, Proc. 14th Winter Sch., Srnî/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

Keywords:

trace; filtration; generalized Lefschetz number; uniform Hausdorff spaces with a filtration; approximate fixed point