Opuscula Math. 38, no. 4 (2018), 463-482

Opuscula Mathematica

Positive definite functions and dual pairs of locally convex spaces

Daniel Alpay
Saak Gabriyelyan

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.

Mathematics Subject Classification: 42A82, 47A20, 47A68.

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  • Daniel Alpay
  • Department of Mathematics, Chapman University, One University Drive Orange, California 92866, USA
  • Saak Gabriyelyan
  • Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be'er Sheva 84105, Israel
  • Communicated by Palle E.T. Jorgensen.
  • Received: 2017-03-28.
  • Accepted: 2017-08-23.
  • Published online: 2018-04-11.
Opuscula Mathematica - cover

Cite this article as:
Daniel Alpay, Saak Gabriyelyan, Positive definite functions and dual pairs of locally convex spaces, Opuscula Math. 38, no. 4 (2018), 463-482, https://doi.org/10.7494/OpMath.2018.38.4.463

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