ABSTRACT
The Leray Schauder degree theory is very useful in solving an operator equation of the type (I − T )x = y, where T is compact. In many applications T is not compact, so one may ask it is possible to give an analogue of the Leray Schauder theory in the noncompact case. In 1936, Leray [184] constructed an example to show that it is impossible to define a degree theory for mappings with only a continuity condition. So a very natural question which arises is the following:
For what kind of mappings in infinite dimensional spaces can we establish a degree theory ?
