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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-2,
author = {Flavius Pater and Tudor B\^\i nzar},
title = {On some dilation theorems for positive definite operator valued functions},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {109-122},
zbl = {1328.47013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-2}
}
Flavius Pater; Tudor Bînzar. On some dilation theorems for positive definite operator valued functions. Studia Mathematica, Tome 231 (2015) pp. 109-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-2-2/