no. 9
Complex analysis/Functional analysis
Weighted composition operators that are complex symmetric on the Fock space F2(Cn)
[Opérateurs de composition à poids qui sont symétriques complexes sur l'espace de Fock F2(Cn)]

Présenté par : Jean-Pierre Demailly

Hai, Pham Viet1 ; Khoi, Le Hai1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore, Singapore
Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 896-900.

Nous étudions les opérateurs de composition à poids sur l'espace de Fock des fonctions entières à plusieurs variables, dans le cas où ces opérateurs sont complexes symétriques. Une formule générale de conjugaison pour ces opérateurs est donnée, et un critère pour que ces opérateurs soient complexes symétriques est obtenu.

We investigate which weighted composition operators can be complex symmetric on the Fock space of entire functions of several variables. A general formula of the so-called weighted composition conjugations is given, and a criterion for weighted composition operators to be complex symmetric is obtained.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.07.006
Hai, Pham Viet 1 ; Khoi, Le Hai 1

1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore, Singapore 
@article{CRMATH_2016__354_9_896_0,
     author = {Hai, Pham Viet and Khoi, Le Hai},
     title = {Weighted composition operators that are complex symmetric on the {Fock} space $ {\mathcal{F}}^{2}({\mathbb{C}}^{n})$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {896--900},
     publisher = {Elsevier},
     volume = {354},
     number = {9},
     year = {2016},
     doi = {10.1016/j.crma.2016.07.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2016.07.006/}
}
TY  - JOUR
AU  - Hai, Pham Viet
AU  - Khoi, Le Hai
TI  - Weighted composition operators that are complex symmetric on the Fock space $ {\mathcal{F}}^{2}({\mathbb{C}}^{n})$
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 896
EP  - 900
VL  - 354
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2016.07.006/
DO  - 10.1016/j.crma.2016.07.006
LA  - en
ID  - CRMATH_2016__354_9_896_0
ER  - 
%0 Journal Article
%A Hai, Pham Viet
%A Khoi, Le Hai
%T Weighted composition operators that are complex symmetric on the Fock space $ {\mathcal{F}}^{2}({\mathbb{C}}^{n})$
%J Comptes Rendus. Mathématique
%D 2016
%P 896-900
%V 354
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2016.07.006/
%R 10.1016/j.crma.2016.07.006
%G en
%F CRMATH_2016__354_9_896_0
Hai, Pham Viet; Khoi, Le Hai. Weighted composition operators that are complex symmetric on the Fock space $ {\mathcal{F}}^{2}({\mathbb{C}}^{n})$. Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 896-900. doi : 10.1016/j.crma.2016.07.006. http://www.numdam.org/articles/10.1016/j.crma.2016.07.006/

[1] Garcia, S.R.; Hammond, C. Which weighted composition operators are complex symmetric?, Oper. Theory, Adv. Appl., Volume 236 (2014), pp. 171-179

[2] Garcia, S.R.; Putinar, M. Complex symmetric operators and applications, Trans. Amer. Math. Soc., Volume 358 (2006), pp. 1285-1315

[3] Garcia, S.R.; Putinar, M. Complex symmetric operators and applications II, Trans. Amer. Math. Soc., Volume 359 (2007), pp. 3913-3931

[4] Hai, P.V.; Khoi, L.H. Weighted composition operators on Fock spaces Fp(C), Acta Math. Vietnam. (2016) (published online 28 April, 2016) | DOI

[5] Hai, P.V.; Khoi, L.H. Complex symmetry of weighted composition operators on the Fock space, J. Math. Anal. Appl., Volume 433 (2016), pp. 1757-1771

[6] Jung, S.; Kim, Y.; Ko, E.; Lee, J.E. Complex symmetric weighted composition operators on H2(D), J. Funct. Anal., Volume 267 (2014), pp. 323-351

[7] Le, T. Normal and isometric weighted composition operators on the Fock space, Bull. Lond. Math. Soc., Volume 46 (2014), pp. 847-856

[8] Wang, M.; Yao, X. Complex symmetry of weighted composition operators in several variables, Int. J. Math., Volume 27 (2016)

[9] Zhao, L. Invertible weighted composition operators on the Fock space of CN, J. Funct. Spaces (2015)

Cité par Sources :

☆ Supported in part by PHC Merlion Project 1.04.14.