Geodesic
The Index of Product Systems of Hilbert Modules: Two Equivalent Definitions
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 49

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We prove that a conditionally completely positive definite kernel, as the generator of completely positive definite (CPD) semigroup associated with a continuous set of units for a product system over a $C^*$-algebra $\mathcal{B}$, allows a construction of a Hilbert $\mathcal{B}-\mathcal{B}$ module. That construction is used to define the index of the initial product system. It is proved that such definition is equivalent to the one previously given by Ke\v cki\'c and Vujo\v sevi\'c [\emph{On the index of product systems of Hilbert modules}, Filomat, to appear, ArXiv:1111.1935v1 [math.OA] 8 Nov 2011]. Also, it is pointed out that the new definition of the index corresponds to the one given earlier by Arveson (in the case $\mathcal{B}=\mathbb{C}$).
DOI : 10.2298/PIM141114001V
Classification : 46L53, 46L55
Keywords: product system, Hilbert module, index 
@article{10_2298_PIM141114001V,
     author = {Biljana Vujo\v{s}evi\'c},
     title = {The {Index} of {Product} {Systems} of {Hilbert} {Modules:} {Two} {Equivalent} {Definitions}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {49 },
     publisher = {mathdoc},
     volume = {_N_S_97},
     number = {111},
     year = {2015},
     doi = {10.2298/PIM141114001V},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM141114001V/}
}
TY  - JOUR
AU  - Biljana Vujošević
TI  - The Index of Product Systems of Hilbert Modules: Two Equivalent Definitions
JO  - Publications de l'Institut Mathématique
PY  - 2015
SP  - 49 
VL  - _N_S_97
IS  - 111
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2298/PIM141114001V/
DO  - 10.2298/PIM141114001V
LA  - en
ID  - 10_2298_PIM141114001V
ER  - 
%0 Journal Article
%A Biljana Vujošević
%T The Index of Product Systems of Hilbert Modules: Two Equivalent Definitions
%J Publications de l'Institut Mathématique
%D 2015
%P 49 
%V _N_S_97
%N 111
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2298/PIM141114001V/
%R 10.2298/PIM141114001V
%G en
%F 10_2298_PIM141114001V
Biljana Vujošević. The Index of Product Systems of Hilbert Modules: Two Equivalent Definitions. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 49 . doi: 10.2298/PIM141114001V

Cité par Sources :