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
Streszczenie
The aim of this paper is to prove dilation theorems for operators from a linear complex space to its -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.
