On the equivalence of multiplicity and the generalized topological degree

Abstract

In this paper we first extend the definition of the multiplicity (as defined by J. Cronin-Scanlon) of operators of the form I + C + T I + C + T to operators of the form H + C + T H + C + T . We then show that the generalized topological degree (as defined by F. E. Browder and W. V. Petryshyn) of operators of the form H + C + T H + C + T is also defined. Finally, we show that when both the multiplicity and generalized topological degree of H + C + T H + C + T are defined, they are equal.