On some dilation theorems for positive definite operator valued functions
Tom 228 / 2015
Studia Mathematica 228 (2015), 109-122 MSC: Primary 47A20; Secondary 47A56. DOI: 10.4064/sm228-2-2
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 $\varGamma $ 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 $\varGamma $ on a $Z$-Loynes space. There is also an algebraic counterpart of this result.