16 research outputs found
Every maximally monotone operator of Fitzpatrick-Phelps type is actually of dense type
We show that every maximally monotone operator of Fitzpatrick-Phelps type
defined on a real Banach space must be of dense type. This provides an
affirmative answer to a question posed by Stephen Simons in 2001 and implies
that various important notions of monotonicity coincide.Comment: 8 page
The Br\'ezis-Browder Theorem in a general Banach space
During the 1970s Br\'ezis and Browder presented a now classical
characterization of maximal monotonicity of monotone linear relations in
reflexive spaces. In this paper, we extend and refine their result to a general
Banach space.Comment: 23 page
Linear -positive sets and their polar subspaces
In this paper, we define a Banach SNL space to be a Banach space with a
certain kind of linear map from it into its dual, and we develop the theory of
linear -positive subsets of Banach SNL spaces with Banach SNL dual spaces.
We use this theory to give simplified proofs of some recent results of
Bauschke, Borwein, Wang and Yao, and also of the classical Brezis-Browder
theorem.Comment: 11 pages. Notational changes since version
Structure theory for maximally monotone operators with points of continuity
In this paper, we consider the structure of maximally monotone operators in
Banach space whose domains have nonempty interior and we present new and
explicit structure formulas for such operators. Along the way, we provide new
proofs of the norm-to-weak closedness and of property (Q) for these
operators (as recently proven by Voisei). Various applications and limiting
examples are given.Comment: 25 page
Banach SSD spaces and classes of monotone sets
In this paper, we unify the theory of SSD spaces and the theory of strongly
representable sets, and we apply our results to the theory of the various
classes of maximally monotone sets. In particular, we prove that type (ED),
dense type, type (D), type (NI) and strongly representable are equivalent
concepts and, consequently, that the known properties of strongly representable
sets follow from known properties of sets of type (ED).Comment: 32 page