Comptes Rendus
no. 9
Complex analysis/Functional analysis
Weighted composition operators that are complex symmetric on the Fock space F2(Cn)

Presented by: Jean-Pierre Demailly

Pham Viet Hai1; Le Hai Khoi1
1 Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University (NTU), 637371 Singapore, Singapore
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 896-900.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.07.006

Pham Viet Hai 1; Le Hai Khoi 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 = {Pham Viet Hai and Le Hai Khoi},
     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},
}
TY  - JOUR
AU  - Pham Viet Hai
AU  - Le Hai Khoi
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
DO  - 10.1016/j.crma.2016.07.006
LA  - en
ID  - CRMATH_2016__354_9_896_0
ER  - 
%0 Journal Article
%A Pham Viet Hai
%A Le Hai Khoi
%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
%R 10.1016/j.crma.2016.07.006
%G en
%F CRMATH_2016__354_9_896_0
Pham Viet Hai; Le Hai Khoi. Weighted composition operators that are complex symmetric on the Fock space $ {\mathcal{F}}^{2}({\mathbb{C}}^{n})$. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 896-900. doi : 10.1016/j.crma.2016.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.006/

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

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

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

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

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

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

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

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

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

Cited by Sources:

☆ Supported in part by PHC Merlion Project 1.04.14.

Comments - Policy