Geodesic
On some dilation theorems for positive definite operator valued functions
Flavius Pater 1   ; Tudor Bînzar 1
1 Department 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

Voir la notice de l'article

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 
@article{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},
     pages = {109--122},
     year = {2015},
     volume = {228},
     number = {2},
     doi = {10.4064/sm228-2-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm228-2-2/}
}
TY  - JOUR
AU  - Flavius Pater
AU  - Tudor Bînzar
TI  - On some dilation theorems for positive definite operator valued functions
JO  - Studia Mathematica
PY  - 2015
SP  - 109
EP  - 122
VL  - 228
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm228-2-2/
DO  - 10.4064/sm228-2-2
LA  - en
ID  - 10_4064_sm228_2_2
ER  - 
%0 Journal Article
%A Flavius Pater
%A Tudor Bînzar
%T On some dilation theorems for positive definite operator valued functions
%J Studia Mathematica
%D 2015
%P 109-122
%V 228
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm228-2-2/
%R 10.4064/sm228-2-2
%G en
%F 10_4064_sm228_2_2
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

Cité par Sources :