Abstract

Estimates for the measure of noncompactness of bounded subsets of spaces of (Bochner-) integrable functions are obtained, a new class of condensing operators is discussed, and the solvability of a certain operator equation in a Hilbert space is proved.

Keywords: Hilbert space, regular space, Lebesgue space, Bochner space, Sobolev space, embedding operator, measure of noncompactness.

MSC: 47H09, 46E35, 47B07, 47B38

Pages:  207--214     

Volume  49 ,  Issue  3$-$4 ,  1997