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Journal of Convex Analysis 18 (2011), No. 1, 227--258
Copyright Heldermann Verlag 2011

Banach SSD Spaces and Classes of Monotone Sets

Stephen Simons
Department of Mathematics, University of California, Santa Barbara, CA 93106-3080, U.S.A.

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).

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