On some dilation theorems for positive definite operator valued functions

Flavius Pater, and Tudor Bînzar. "On some dilation theorems for positive definite operator valued functions." Studia Mathematica 228.2 (2015): 109-122. <http://eudml.org/doc/285752>.

@article{FlaviusPater2015,
abstract = {The aim of this paper is to prove dilation theorems for operators from a linear complex space to its Z-anti-dual space. The main result is that a bounded positive definite function from a *-semigroup Γ into the space of all continuous linear maps from a topological vector space X to its Z-anti-dual can be dilated to a *-representation of Γ on a Z-Loynes space. There is also an algebraic counterpart of this result.},
author = {Flavius Pater, Tudor Bînzar},
journal = {Studia Mathematica},
keywords = {positive definiteness; Loynes spaces; dilation theorems},
language = {eng},
number = {2},
pages = {109-122},
title = {On some dilation theorems for positive definite operator valued functions},
url = {http://eudml.org/doc/285752},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Flavius Pater
AU - Tudor Bînzar
TI - On some dilation theorems for positive definite operator valued functions
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 2
SP - 109
EP - 122
AB - The aim of this paper is to prove dilation theorems for operators from a linear complex space to its Z-anti-dual space. The main result is that a bounded positive definite function from a *-semigroup Γ into the space of all continuous linear maps from a topological vector space X to its Z-anti-dual can be dilated to a *-representation of Γ on a Z-Loynes space. There is also an algebraic counterpart of this result.
LA - eng
KW - positive definiteness; Loynes spaces; dilation theorems
UR - http://eudml.org/doc/285752
ER -