caa a22 4500 388092130 CHVBK 20180307125254.0 cr unu---uuuuu 161130e199908 xx s 000 0 eng 10.1017/S0004972700033426 doi S0004972700033426 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700033426 Stronger maximal monotonicity properties of linear operators [Elektronische Daten] The subdifferential mapping associated with a proper, convex lower semicontinuous function on a real Banach space is always a special kind of maximal monotone operator. Specifically, it is always "strongly maximal monotone” and of "type (ANA)”. In an attempt to find maximal monotone operators that do not satisfy these properties, we investigate (possibly discontinuous) maximal monotone linear operators from a subspace of a (possibly nonreflexive) real Banach space into its dual. Such a linear mapping is always "strongly maximal monotone”, but we are only able to prove that is of "type (ANA)” when it is continuous or surjective — the situation in general is unclear. In fact, every surjective linear maximal monotone operator is of "type (NA)”, a more restrictive condition than "type (ANA)”, while the zero operator, which is both continuous and linear and also a subdifferential, is never of "type (NA)” if the underlying space is not reflexive. We examine some examples based on the properties of derivatives. Copyright © Australian Mathematical Society 1999 Bauschke H.H. Department of Mathematics and Statistics Okanagan University College 3333 College Way Kelowna, BC V1V 1V7 Canada e-mail: bauschke@cecm.sfu.ca Simons S. E-mail: simons@math.ucsb.edu Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 163-174 0004-9727 60:1<163 1999 60 BAZ https://doi.org/10.1017/S0004972700033426 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700033426 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bauschke H.H. Department of Mathematics and Statistics Okanagan University College 3333 College Way Kelowna, BC V1V 1V7 Canada e-mail: bauschke@cecm.sfu.ca NATIONALLICENCE 700 1- Simons S. E-mail: simons@math.ucsb.edu NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/1(1999-08), 163-174 0004-9727 60:1<163 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge