  We discuss "Banach SN spaces", which include Hilbert spaces, negative Hilbert
spaces, and the product of any real Banach space with its dual. We introduce
"L-positive" sets, which generalize monotone multifunctions from a Banach space
into its dual. We introduce the concepts of "$r_L$-density" and its
specialization "quasidensity": the closed quasidense monotone multifunctions
from a Banach space into its dual form a (generally) strict subset of the
maximally monotone ones, though all surjective maximally monotone and all
maximally monotone multifunctions on a reflexive space are quasidense. We give
a sum theorem and a parallel sum theorem for closed monotone quasidense
multifunctions under very general constraint conditions. That is to say,
quasidensity obeys a very nice calculus rule. We give a short proof that the
subdifferential of a proper convex lower semicontinuous function on a Banach
space is quasidense, and deduce generalizations of the Brezis-Browder theorem
on linear relations to non reflexive Banach spaces. We also prove that any
closed monotone quasidense multifunction has a number of other very desirable
properties. This version differs from the previous version in the removal of
Sections 13-16, part of Section 17, and Section 18.
