  This paper is about certain linear subspaces of Banach SN spaces (that is to
say Banach spaces which have a symmetric nonexpansive linear map into their
dual spaces). We apply our results to monotone linear subspaces of the product
of a Banach space and its dual. In this paper, we establish several new results
and also give improved proofs of some known ones in both the general and the
special contexts.
