1,109 research outputs found
SSDB spaces and maximal monotonicity
In this paper, we develop some of the theory of SSD spaces and SSDB spaces,
and deduce some results on maximally monotone multifunctions on a reflexive
Banach space.Comment: 16 pages. Written version of the talk given at IX ISORA in Lima,
Peru, October 200
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
Maximality of the sum of a maximally monotone linear relation and a maximally monotone operator
The most famous open problem in Monotone Operator Theory concerns the maximal
monotonicity of the sum of two maximally monotone operators provided that
Rockafellar's constraint qualification holds.
In this paper, we prove the maximal monotonicity of provided that are maximally monotone and is a linear relation, as soon as
Rockafellar's constraint qualification holds: \dom A\cap\inte\dom
B\neq\varnothing. Moreover, is of type (FPV).Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:1010.4346, arXiv:1005.224
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
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