GRANT CNCSIS (Consiliul National al Cercetarii Stiintifice din
Invatamantul Superior)
Cod A 1065/2006
Director proiect: Lect. dr.
Maria Joita, Universitatea
Bucuresti, E-mail: [email protected]
Membrii echipei:
1.
Conf. dr. Alexandra
Colojoara, Universitatea
Bucuresti, E-mail: [email protected]
2.
Conf. dr. Madalina
Buneci,
Universitatea Constantin Brancusi din Targul-Jiu, E-mail: [email protected]
3.
Asist. dr. Roxana
Vidican, Universitatea
Politehnica Bucuresti, E-mail: [email protected]
4.
Asist. drd. Tania -
Luminita Costache, Universitatea
Politehnica Bucuresti , E-mail: [email protected]
5.
Asist. drd. Mariana
Zamfir, Universitatea
Tehnica de Constructii Bucuresti, E-mail: [email protected]
6.
Asist. drd. Radu
Munteanu, Universitatea
Bucuresti, E-mail: [email protected]
- Rezumat:
Conceptul de ordine
matriceala joaca un rol foarte important pentru intelegerea structurii
necomutative a algebrelor de operatori. Ca o atasare naturala la aceasta
structura de ordine, aplicatiile liniare complet pozitive sunt intens studiate.
Rezultatele obtinute in studiul a plicatiilor complet pozitive si al celor
complet marginite au multe aplicatii: teoria C* -extensiilor; teoria
dilatarii; K -teorie si KK -teorie; fizica matematica; teoria informatiei
cuantice.
Matematic, in teoria informatiei cuantice asa numitele operatii cuantice
sunt reprezentate de aplicatii liniare complet pozitive contractive intre
algebrele observabilelor (reprezentate prin C* -algebre ) asociate
sistemelor fizice considerate. Teoremele de structura si teoremele de tip
Radon-Nikodym pentru aplicatii liniare complet pozitive sunt un instrument de
lucru foarte important in teoria informatiei cuantice, mai ales in rezolvarea
si intelegerea unor probleme care presupun caracterizarea si compararea
operatiilor cuantice.
Scopul principal al acestui proiect este obtinerea de rezultate noi
privind structura aplicatiilor liniare complet (multi-) pozitive intre C*-algebre
(C*-algebre locale) si caraacterizarea relatiei de ordine pe multimea
aplicatiilor complet pozitive intre C* -algebre (C*-algebre
locale) in functie de structura aceestora.
- Rapoarte: Sinteza
lucrarii 2006
- Lista lucrarilor (partial) suportate din acest grant:
A.
Comunicari:
1. M. Joita, T- L. Costache, M. Zamfir, International Conference on Mathematics and
Informatics, ICMI 45,
2. M. Joita, T- L. Costache, M. Zamfir, The 4 -th International Colloquium Mathematics in
Engineering and Numerical Physics, MENP -4, October 6 - 8, 2006, University
Politehnica of Bucharest, Romania. Titlul comunicarii: Dilations on Hilbert C* -modules for dynamical C*
-systems
3. A. Colojoara,
The 4 -th International Colloquium Mathematics in Engineering and Numerical
Physics, MENP-4,
4. R. Munteanu,
The International Workshop on Operator Models and Applications (OMA) 2006,
5. M. Joita,
III Workshop on Coverings, Selections and Games in Topology, April 25-29, 2007
Faculty of Sciences and Mathematics, Nis; Technical Faculty, Cacak Serbia,
Titlul comunicarii: On frames
in Hilbert modules over pro-C*-algebras
6. M. Joita, L-T.
Costache, M. Zamfir, III Workshop on Coverings, Selections and Games
in Topology, April 25-29, 2007 Faculty of Sciences and Mathematics, Nis;
Technical Faculty, Cacak Serbia, Titlul comunicarii: Covariant representation associated with
covariant completely n-positive linear maps between C*-algebras
7. M. Joita, L-T. Costache, M. Zamfir, (ICTCAM 2007) International Conference "Trends
and Challenges in Applied Mathematics" June 20-23,2007, Bucharest, Romania,
Titlul comunicarii: On the
order structure on the set of completely n-positive linear maps on C*-algebras
8.
M. Joita,The 6th Congress of Romanian Mathematicians, Romania,
University of Bucharesti, June 28-July 4, 2007. Titlul comunicarii: Extremal completely n-positive linear maps
between C*-algebras (partial)
9. M. Joita, L-T. Costache, M. Zamfir, 22nd Summer Conference on Topology and Its
Applications, July 24-27, 2007,Castellón, Spain, Titlul comunicarii: Characterization of the order relation on
the set of completely n-positive linear maps between C*-algebras
10. M. Joita,
Departamentul de Matematica, Universitatea din Atena, Grecia, 19 Septembrie,
Titlul conferintei: Hilbert
modules over pro-C*-algebras and operators on Hilbrt modules over pro-C*-algebras
11. M. Joita, Departamentul de Matematica, Universitatea din
Atena, Grecia, 25 Septembrie, Titlul conferintei: Tensor products of Hilbert modules over
pro-C*-algebras
12. M.
Joita, Fifty International Conference of Applied Mathematics and Computing,
12-18 August 2008, Plovdiv, Bulgaria, Titlul comunicarii: On group actions on pro-C*-algebras
13. M. Joita, The 20th International Congress of
Jangjeon Mathematical Society, 21-23 August 2008, Uludag University,
Bursa-Turkey, Titlul comunicarii: Morita equivalence and outer conjugacy of dynamical systems
14. M.
Buneci, The 20th
International Congress of Jangjeon Mathematical Society, 21-23 August 2008,
Uludag University, Bursa-Turkey, Titlul comunicarii: A generalization of Zakrewski morphisms
15. M. Olteanu,
L-T. Costache, M. Zamfir, Fifty
International Conference of Applied Mathematics and Computing, 12-18 August
2008, Plovdiv, Bulgaria, Titlul comunicarii: On the
computation of the spectra of a class of convolution operators
B. Lucrari realizate:
a)
Articole stiintifice
1. M. Joita, Completely multi-positive linear maps
between locally C*-algebras and representations on Hilbert modules, Studia Math., 172 (2006), 181-196, (revista cotata ISI).
2. M. Joita, Crossed
products of locally C*-algebras, Rocky Math. J., 37
(2007), 5, (revista
cotata ISI), math. OA/0512128 (partial)
3. M. Joita, Covariant completely positive linear maps on locally C*
-algebras and representations on Hilbert mmoddules, Huston J. Math. (33(2007),4,
1067-1078, (revista cotata
ISI), math.OA/0609149.
4. M. Joita,
Covariant completely
n-positive linear maps on pro-C*-algebras, Chinese Annals of
Mathematics, Series B, 13(2008), 1, 55-64, (revista cotata ISI)
5. M. Joita, A Radon-Nikodym theorem for completely
multi-positive linear maps and its applications, Contemp. Math., 427(2007), 235--245, Amer.
Math. Soc., Providence, Proceedings of the 5th International Conference on
Topological Algebra and Applications, University of Athens, Greece, June 27-
July 1, 2005, Edited by A. Mallios and M. Haralampidou), (proceedings ISI), math.OA/0510073
6. M. Joita, A Radon-Nikodym theorem for completely
multi-positive linear maps on pro-C*-algebras and its applications, Publicationes
Mathematicae Debrecen, 72(2008), 1-2, 55-67, (revista cotata ISI),
math.OA/0701263.
7. M. Joita, On tensor products of completely positive
linear maps between pro-C*-algebras, Positivity,
Online First 2008, Birkhäauser Verlag
Basel/Switzerland DOI 10.1007/s11117-008-2147-5, (revista cotata ISI)
(partial)
8. M. Joita, On frames in Hilbert modules over
pro-C*-algebras, Topology and its
Applications doi:10.1016/j.topol.2007.12.015 (revista cotata ISI) (Proceedings of the IIIrd Workshop on Coverings,
Selections and Games in Topology, April 25-29, 2007, Serbia), arXiv:0709.0796v1
9. M. Joita, On multipliers of Hilbert modules over pro-C*-algebras, Studia
Math. 185(2008), 3, 263-277, (revista cotata ISI)
10. M .
Joita, On
representations of Banach C*-modules associated with biweights, (trimisa pentru
publicare).
11. M. Joita, A
note about full Hilbert modules over Frechet locally C*-algebras, Novi Sad Journal of Mathematics, 37(2007), 1, 27-32.
12. M.
Joita, Multipliers modules, countably generated Hilbert modules and stable
isomorphisms of locally C*-algebras,
Hot Topics in Operator Theory (Proceedings of The 21st International Conference on
Operator Theory,Timisoara, Jiune 29-July 4), 2006), 89-99, Theta Ser. Adv.
Math. 9, Theta, Bucharest, 2008, eds (R.G. Douglas, J. Estrele, D. Gaspar, D.
Timotin, F-H Vasilescu) (partial)
13. M. Joita, On
extremal covariant completely n-positive linear maps, Proceedings of The 6th Congress of Romanian
Mathematicians, Romania, University of Bucharest, June 28-July 4, 2007
(acceptat pentru publicare) (partial)
14. M. Joita,
T- L. Costache, M. Zamfir, Representations associated with completely n-positive linear
maps between C* -algebras, Stu. Cercet. Stiint. Ser. Mat.
16(2006), 111-122 (Proceedings of International Conference on Mathematics
and Informatics, ICMI 45 Bacau, Romania, September 18 - 20, 2006).
15. M. Joita, T- L. Costache, M. Zamfir, Dilations
on Hilbert C* -modules for dynamical C*-systems, Proceedings
of The 4 -th International Colloquium Mathematics in Engineering and Numerical
Physics , MENP -4,
16. M. Joita,
L-T. Costache, M. Zamfir, On the order structure on the set of
completely n-positive linear maps on C*-algebras, Glasnik Matematicki (acceptat pentru publicare).
17. M. Joita,
L-T. Costache, M. Zamfir, Characterization of the order relation on
the set of completely n-positive linear maps between C*-algebras, Surveys in Mathematics and its Applications
2(2008), 113-122.
18. M. Buneci, Haar systems compatible with groupoid morphisms, An. Univ. Timisoara Ser.Mat.-Inform., 44(2006) no. 2, 19-32 [ISSN1224-970X] (partial).
19. M. Buneci, Groupoid C*-algebras, Surveys in
Mathematics and its Applications (Proceedings of International Workshop
"Operator Models and Applications- OMA 2006"), p. 71-98.(partial).
20. R.
Vidican, Irreducible covariant
representations associated wit an r-discrete groupoid, Politehn.
Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 69(2007),2, 17-26.
21. A.
Colojoara, Positive Operators on Time Series, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl.
Math. Phys. (trimisa pentru
publicare).
22. A.
Colojoara, Symmetric Algebra of L(X,F) as an Algebra
of Polynomials, Hot Topics in
Operator Theory (Proceedings of The 21st International Conference on
Operator Theory,Timisoara, Jiune 29-July 4), 2006), 59-68, Theta Ser. Adv.
Math. 9, Theta, Bucharest, 2008, eds (R.G. Douglas, J. Estrele, D. Gaspar, D.
Timotin, F-H Vasilescu) (partial)
b) Carti
1.
M. Joita, Completely positive linear maps on
pro-C*-algebras, Editura Universitatii din Bucuresti,
110 pg., ISBN 978-973-737-530-8
2.
M. Joita, Crossed products of locally C*-algebras, Editura Academiei Romane, 126+Xii pg,, ISBN
978-973-27-1600-7 (partial)
