Positive definite functions and dual pairs of locally convex spaces

Positive definite functions and dual pairs of locally convex spaces

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.

Bibliographic Details
Main Authors: Daniel Alpay, Saak Gabriyelyan
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2018-01-01
Series:Opuscula Mathematica
Subjects:
positive definite function
locally convex space
dual pair
the (strong) factorization property
dilation theory
Online Access:http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3821.pdf
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spelling doaj-1b0056f339824ab9904a1eadf093304e2020-11-25T00:49:54ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01384463482https://doi.org/10.7494/OpMath.2018.38.4.4633821Positive definite functions and dual pairs of locally convex spacesDaniel Alpay0Saak Gabriyelyan1Department of Mathematics, Chapman University, One University Drive Orange, California 92866, USADepartment of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be'er Sheva 84105, IsraelUsing 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.http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3821.pdfpositive definite functionlocally convex spacedual pairthe (strong) factorization propertydilation theory
collection DOAJ
language English
format Article
sources DOAJ
author Daniel Alpay
Saak Gabriyelyan
spellingShingle Daniel Alpay
Saak Gabriyelyan
Positive definite functions and dual pairs of locally convex spaces
Opuscula Mathematica
positive definite function
locally convex space
dual pair
the (strong) factorization property
dilation theory
author_facet Daniel Alpay
Saak Gabriyelyan
author_sort Daniel Alpay
title Positive definite functions and dual pairs of locally convex spaces
title_short Positive definite functions and dual pairs of locally convex spaces
title_full Positive definite functions and dual pairs of locally convex spaces
title_fullStr Positive definite functions and dual pairs of locally convex spaces
title_full_unstemmed Positive definite functions and dual pairs of locally convex spaces
title_sort positive definite functions and dual pairs of locally convex spaces
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2018-01-01
description 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.
topic positive definite function
locally convex space
dual pair
the (strong) factorization property
dilation theory
url http://www.opuscula.agh.edu.pl/vol38/4/art/opuscula_math_3821.pdf
work_keys_str_mv AT danielalpay positivedefinitefunctionsanddualpairsoflocallyconvexspaces
AT saakgabriyelyan positivedefinitefunctionsanddualpairsoflocallyconvexspaces
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