A Note on Some Extensions of Monotone Operators to the Bidual

The paper has a double aim. On the one hand, it studies some monotone extensions to the bidual of monotone operators which are not of type (D), paying particular attention to the issue of representability of these extensions by means of convex functions. On the other hand, it derives a density property for maximal monotone operators that, not only are of type (D), but have their unique maximal monotone extensions to the bidual which are of type (D) as well, as it is the case for subdifferentials of lower semicontinuous convex functions.