Geodesic
The complete hyperexpansivity analog of the Embry conditions
Ameer Athavale1
1 Department of Mathematics University of Pune Pune 411007, India
Studia Mathematica, Tome 154 (2003) no. 3, pp. 233-242

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The Embry conditions are a set of positivity conditions that characterize subnormal operators (on Hilbert spaces) whose theory is closely related to the theory of positive definite functions on the additive semigroup ${{\mathbb N}}$ of non-negative integers. Completely hyperexpansive operators are the negative definite counterpart of subnormal operators. We show that completely hyperexpansive operators are characterized by a set of negativity conditions, which are the natural analog of the Embry conditions for subnormality. While the genesis of the Embry conditions can be traced to the Hausdorff Moment Problem, the genesis of the conditions to be established here lies in the L{é}vy–Khinchin representation as holding in the context of abelian semigroups. We actually establish the desired negativity criteria for completely hyperexpansive operator tuples.
DOI : 10.4064/sm154-3-4
Keywords: embry conditions set positivity conditions characterize subnormal operators hilbert spaces whose theory closely related theory positive definite functions additive semigroup mathbb non negative integers completely hyperexpansive operators negative definite counterpart subnormal operators completely hyperexpansive operators characterized set negativity conditions which natural analog embry conditions subnormality while genesis embry conditions traced hausdorff moment problem genesis conditions established here lies khinchin representation holding context abelian semigroups actually establish desired negativity criteria completely hyperexpansive operator tuples

Ameer Athavale 1

1 Department of Mathematics University of Pune Pune 411007, India 
@article{10_4064_sm154_3_4,
     author = {Ameer Athavale},
     title = {The complete hyperexpansivity analog
 of the {Embry} conditions},
     journal = {Studia Mathematica},
     pages = {233--242},
     publisher = {mathdoc},
     volume = {154},
     number = {3},
     year = {2003},
     doi = {10.4064/sm154-3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm154-3-4/}
}
TY  - JOUR
AU  - Ameer Athavale
TI  - The complete hyperexpansivity analog
 of the Embry conditions
JO  - Studia Mathematica
PY  - 2003
SP  - 233
EP  - 242
VL  - 154
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm154-3-4/
DO  - 10.4064/sm154-3-4
LA  - en
ID  - 10_4064_sm154_3_4
ER  - 
%0 Journal Article
%A Ameer Athavale
%T The complete hyperexpansivity analog
 of the Embry conditions
%J Studia Mathematica
%D 2003
%P 233-242
%V 154
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm154-3-4/
%R 10.4064/sm154-3-4
%G en
%F 10_4064_sm154_3_4
Ameer Athavale. The complete hyperexpansivity analog
 of the Embry conditions. Studia Mathematica, Tome 154 (2003) no. 3, pp. 233-242. doi: 10.4064/sm154-3-4

Cité par Sources :