ON STRONGLY CONDENSING OPERATORS AT INFINITY

Abstract

The paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptotic derivative is compact. In particular, this notion allows to build examples of operators that are neither compact, nor condensing, not even -bounded. Such operators form a linear space. Some applications of the notion to the theory of bifurcation points are discussed.

Keywords

• measure of noncompactness
• condensing operator
• locally strongly condensing operator
• asymptotically linear operator
• asymptotic derivative
• bifurcation point