Comptes Rendus
Functional Analysis
New constructions of homogeneous operators
[Nouvelles constructions d'opérateurs homogènes]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 933-936.

New examples of homogeneous operators involving infinitely many parameters are constructed. They are realized on Hilbert spaces of holomorphic functions with reproducing kernels which are computed explicitly. All the examples are irreducible and belong to the Cowen–Douglas class. Even though the construction is completely explicit, it is based on certain facts about Hermitian holomorphic homogeneous vector bundles. These facts also make possible a description of all homogeneous Cowen–Douglas operators, in a somewhat less explicit way.

Ou construit une nouvelle famille d'examples d'opérateurs homogènes dépendant d'une infinité de paramètres. Les exemples sont réalisés sur des espaces de fonctions holomorphes possédant des noyaux reproduisants qu'on calcule explicitement. Les exemples sont tous des opérateurs irréductibles appartenant à la classe de Cowen–Douglas. Tout en étant complètement explicite, la construction est fondée sur certaines propriétés des fibrés vectoriels hermitiens holomorphes homogènes. Ces propriétés permettent aussi une description, un peu moins explicite, de tous les opérateurs homogènes de la classe de Cowen–Douglas.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.04.002

Adam Korányi 1 ; Gadadhar Misra 2

1 Lehman College, Bronx, NY 10468, USA
2 Indian Statistical Institute, R. V. College Post, Bangalore 560 059, India
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Adam Korányi; Gadadhar Misra. New constructions of homogeneous operators. Comptes Rendus. Mathématique, Volume 342 (2006) no. 12, pp. 933-936. doi : 10.1016/j.crma.2006.04.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.002/

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  • Yufang Xie; Kui Ji Operators of the Cowen–Douglas class with strong flag structure, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, Volume 118 (2024) no. 3 | DOI:10.1007/s13398-024-01630-y
  • Borislava Bekker; Miron B. Bekker On Selfadjoint Homogeneous Operators, Complex Analysis and Operator Theory, Volume 7 (2013) no. 1, p. 9 | DOI:10.1007/s11785-011-0175-9
  • Amritanshu Prasad; M. K. Vemuri Inductive Algebras and Homogeneous Shifts, Complex Analysis and Operator Theory, Volume 4 (2010) no. 4, p. 1015 | DOI:10.1007/s11785-009-0020-6
  • INDRANIL BISWAS; GADADHAR MISRA SL(2,R)~-HOMOGENEOUS VECTOR BUNDLES, International Journal of Mathematics, Volume 19 (2008) no. 01, p. 1 | DOI:10.1142/s0129167x08004534
  • Adam Korányi; Gadadhar Misra Homogeneous operators on Hilbert spaces of holomorphic functions, Journal of Functional Analysis, Volume 254 (2008) no. 9, p. 2419 | DOI:10.1016/j.jfa.2007.12.014
  • Harald Upmeier Toeplitz Operator Algebras and Complex Analysis, Operator Algebras, Operator Theory and Applications, Volume 181 (2008), p. 67 | DOI:10.1007/978-3-7643-8684-9_3
  • Gadadhar Misra; Subrata Shyam Roy On the Irreducibility of a Class of Homogeneous Operators, System Theory, the Schur Algorithm and Multidimensional Analysis (2007), p. 165 | DOI:10.1007/978-3-7643-8137-0_3
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