Partial Inner Product Structures on Certain Topological Vector Lattices
Jean-Pierre Antoine, Gisela A. Lassner Β· Mathematische Nachrichten Β· 1984
We study the order structure induced on a rigged Hilbert space π β Ο βͺ πβ²by a self-dual cone in Ο. Under the assumption that π is a semi-reflexive locally convex vector lattice, and a solid subset of πβ² (we speak then of a rigged Hilbert lattice), we show that πβ² is in fact a nondegenerate partial inner product space.