La description explicite des opérateurs homogènes et la localisation d'un module de Hilbert conduit naturellement à la définition d'une classe d'opérateurs de Cowen–Douglas possédant une structure flag. Ces opérateurs sont irréductibles. Nous montrons que la structure flag est rigide en ce sens que la classe d'équivalence unitaire de l'opérateur et la structure du pavillon se déterminent l'une l'autre. Nous obtenons un ensemble complet d'invariants unitaires qui sont un peu plus dociles que ceux d'un opérateur arbitraire dans la classe de Cowen–Douglas.
The explicit description of homogeneous operators and localization of a Hilbert module naturally leads to the definition of a class of Cowen–Douglas operators possessing a flag structure. These operators are irreducible. We show that the flag structure is rigid in the sense that the unitary equivalence class of the operator and the flag structure determine each other. We obtain a complete set of unitary invariants which are somewhat more tractable than those of an arbitrary operator in the Cowen–Douglas class.
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@article{CRMATH_2014__352_6_511_0,
author = {Ji, Kui and Jiang, Chunlan and Keshari, Dinesh Kumar and Misra, Gadadhar},
title = {Flag structure for operators in the {Cowen{\textendash}Douglas} class},
journal = {Comptes Rendus. Math\'ematique},
pages = {511--514},
publisher = {Elsevier},
volume = {352},
number = {6},
year = {2014},
doi = {10.1016/j.crma.2014.04.001},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.04.001/}
}
TY - JOUR AU - Ji, Kui AU - Jiang, Chunlan AU - Keshari, Dinesh Kumar AU - Misra, Gadadhar TI - Flag structure for operators in the Cowen–Douglas class JO - Comptes Rendus. Mathématique PY - 2014 SP - 511 EP - 514 VL - 352 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.04.001/ DO - 10.1016/j.crma.2014.04.001 LA - en ID - CRMATH_2014__352_6_511_0 ER -
%0 Journal Article %A Ji, Kui %A Jiang, Chunlan %A Keshari, Dinesh Kumar %A Misra, Gadadhar %T Flag structure for operators in the Cowen–Douglas class %J Comptes Rendus. Mathématique %D 2014 %P 511-514 %V 352 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.04.001/ %R 10.1016/j.crma.2014.04.001 %G en %F CRMATH_2014__352_6_511_0
Ji, Kui; Jiang, Chunlan; Keshari, Dinesh Kumar; Misra, Gadadhar. Flag structure for operators in the Cowen–Douglas class. Comptes Rendus. Mathématique, Tome 352 (2014) no. 6, pp. 511-514. doi : 10.1016/j.crma.2014.04.001. http://www.numdam.org/articles/10.1016/j.crma.2014.04.001/
[1] Curvature and similarity, Mich. Math. J., Volume 30 (1983), pp. 361-367
[2] On weighted shifts, curvature and similarity, J. Lond. Math. Soc. (2), Volume 31 (1985), pp. 357-368
[3] Complex geometry and operator theory, Acta Math., Volume 141 (1978), pp. 187-261
[4] On operators possessing an open set of eigenvalues, Memorial Conf. for Féjer-Riesz, Colloq. Math. Soc. János Bolyai, 1980, pp. 323-341
[5] Generalized Bergman kernels and the Cowen–Douglas theory, Amer. J. Math., Volume 106 (1984), pp. 447-488
[6] Similarity of n-hypercontractions and backward Bergman shifts, J. Lond. Math. Soc., Volume 88 (2013), pp. 637-648
[7] Equivalence of quotient Hilbert modules. II, Trans. Amer. Math. Soc., Volume 360 (2008), pp. 2229-2264
[8] Similarity classification of holomorphic curves, Adv. Math., Volume 215 (2007), pp. 446-468
[9] Strongly Irreducible Operators on Hilbert Space, Pitman Research Notes in Mathematics Series, vol. 389, Longman, Harlow, 1998 (x+243 pp)
[10] A classification of homogeneous operators in the Cowen–Douglas class, Adv. Math., Volume 226 (2011), pp. 5338-5360
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