Continuous mappings of open sets in a Banach space

If is a bounded open set of a Banach space (B), is a completely continuous mapping of into the same space (B), and E- , where E is the identity transformation, is a uniformly fading mapping of into the Banach space, then the order of on equals ± 1 at every point y of .Translated from Matematicheskii Zametki, Vol. 13, No. 6, pp. 838–848, June, 1973.In conclusion, the author wishes to express her gratitude to her supervisor, K. A. Sitnikov.