Geodesic
On some dilation theorems for positive definite operator valued functions
Flavius Pater1 ; Tudor Bînzar1
1Department of Mathematics Politehnica University of Timişoara 300006 Timişoara, Romania
Studia Mathematica, Tome 228 (2015) no. 2, pp. 109-122
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm228-2-2
Keywords: paper prove dilation theorems operators linear complex space its z anti dual space main result bounded positive definite function * semigroup vargamma space continuous linear maps topological vector space its z anti dual dilated * representation vargamma z loynes space there algebraic counterpart result

Flavius Pater  1   ; Tudor Bînzar  1

1 Department of Mathematics Politehnica University of Timişoara 300006 Timişoara, Romania 
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Flavius Pater; Tudor Bînzar. On some dilation theorems for positive definite operator valued functions. Studia Mathematica, Tome 228 (2015) no. 2, pp. 109-122. doi: 10.4064/sm228-2-2

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