First, we consider a compact real-analytic irreducible subvariety M in a sphere and its dual variety M. We explain that two matrices of the second fundamental forms for both varieties M and M can be regarded as the inverse matrices of each other. Also generalization in hyperbolic space is explained.

1. Let A be a fixed compact Hausdorff space, C the Banach lattice of continuous real functions on X, L its dual, and M its second dual. The closure of C in M under the weak topology wiM, L) determined by L is, as is well known, M itself. In fact, the closure of C under the Mackey topology riM, L) is M itself, by the Grothendieck Theorem. A deeper property is that this relationship between C and...