Extension problems for accretive sets in Banach spaces

This paper contains both negative and positive results concerning the possibility of extending accretive sets in Banach spaces to m-accretive sets. On the one hand, it is shown that if a closed convex subset C of a reflexive strictly convex Banach space E is not a nonexpansive retract of E, then no accretive A such that clco(D(A)) = C can be extended to an m-accretive set B with D(B) ?C, and that if a non-Hilbert E is reflexive and smooth, then there is an accretive set A ?E × E which has no m-accretive extension. On the other hand, we establish positive results and then apply them to the study of the asymptotic behavior of nonlinear semigroups, the construction of zeros of accretive sets, and the characterization of invariant sets for nonlinear semigroups.