Positive definite functions and dual pairs of locally convex spaces

Abstract

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.

Keywords

• positive definite function
• locally convex space
• dual pair
• the (strong) factorization property
• dilation theory