Enlargements and sums of monotone operators

Generalized sums of two maximal monotone operators and enlargement of such operators were studied. An extended sum concept generated by the enlargements of the operators was used to study the notion of the sum. The extended sum was defined in a general Banach space and the variational sum was extended to the setting of reflexive Banach spaces. The two notions were found to coincide in the case of subdifferentials of convex functions. The subdifferential of the sum of two proper convex lower semicontinuous functions was found to be exactly the extended sum of their subdifferentials.