Compact perturbations of 𝑚-accretive operators in Banach spaces

Abstract

This paper continues a discussion that arose twenty years ago, concerning the perturbation of an m m -accretive operator by a compact mapping in Banach spaces. Indeed, if A A is m m -accretive and g g is compact, then the boundary condition t x ∉ A ( x ) g ( x ) tx \notin A(x)g(x) for x ∈ ∂ G ∩ D ( A ) x \in \partial G \cap D(A) and t > 0 t>0 implies that 0 0 is in the closure of the range of A + g A+g . Perhaps the most interesting aspect of this result is the proof itself, which does not appeal to the classical degree theory argument used for this type of problem.