Surjectivity of linear operators from a Banach space into itself

Abstract

We show that linear operators from a Banach space into itself which satisfy some relaxed strong accretivity conditions are invertible. Moreover, we characterise a particular class of such operators in the Hilbert space case. By doing so we manage to answer a problem posed by B. Ricceri, concerning a linear second order partial differential operator.

On a class of operator equations arising in infinite dimensional replicator dynamics

“…The existence and uniqueness result for the auxiliary equation follows from nonlinear generalizations of the Lax-Milgram lemma (see e.g. [11,7,12]). Concerning the continuity ofφ(λ), assume that u λ i is the solution of A(u λ i ) = λ i , i = 1, 2.…”