For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint

Details For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint For maximally monotone linear relations, dense type, negative-infimum type, and Fitzpatrick-Phelps type all coincide with monotonicity of the adjoint

2011-03-31

arxiv.org/abs/1103.6239v1

Mathematics

Functional Analysis

15 pages

Scientific paper

It is shown that, for maximally monotone linear relations defined on a
general Banach space, the monotonicities of dense type, of negative-infimum
type, and of Fitzpatrick-Phelps type are the same and equivalent to
monotonicity of the adjoint. This result also provides affirmative answers to
two problems: one posed by Phelps and Simons, and the other by Simons.

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