Functional analysis
Flag structure for operators in the Cowen–Douglas class
Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 511-514.

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.

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.

Accepted:
Published online:
DOI: 10.1016/j.crma.2014.04.001

Kui Ji 1; Chunlan Jiang 1; Dinesh Kumar Keshari 2; Gadadhar Misra 3

1 Department of Mathematics, Hebei Normal University, Shijiazhuang, Hebei 050016, China
2 Department of Mathematics, Texas A&M University, College Station, TX 77843, United States
3 Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
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Kui Ji; Chunlan Jiang; Dinesh Kumar Keshari; Gadadhar Misra. Flag structure for operators in the Cowen–Douglas class. Comptes Rendus. Mathématique, Volume 352 (2014) no. 6, pp. 511-514. doi : 10.1016/j.crma.2014.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.04.001/

[1] D.N. Clark; G. Misra Curvature and similarity, Mich. Math. J., Volume 30 (1983), pp. 361-367

[2] D.N. Clark; G. Misra On weighted shifts, curvature and similarity, J. Lond. Math. Soc. (2), Volume 31 (1985), pp. 357-368

[3] M.J. Cowen; R.G. Douglas Complex geometry and operator theory, Acta Math., Volume 141 (1978), pp. 187-261

[4] M.J. Cowen; R.G. Douglas On operators possessing an open set of eigenvalues, Memorial Conf. for Féjer-Riesz, Colloq. Math. Soc. János Bolyai, 1980, pp. 323-341

[5] R.E. Curto; N. Salinas Generalized Bergman kernels and the Cowen–Douglas theory, Amer. J. Math., Volume 106 (1984), pp. 447-488

[6] R.G. Douglas; H.-K. Kwon; S. Treil Similarity of n-hypercontractions and backward Bergman shifts, J. Lond. Math. Soc., Volume 88 (2013), pp. 637-648

[7] R.G. Douglas; G. Misra Equivalence of quotient Hilbert modules. II, Trans. Amer. Math. Soc., Volume 360 (2008), pp. 2229-2264

[8] C. Jiang; K. Ji Similarity classification of holomorphic curves, Adv. Math., Volume 215 (2007), pp. 446-468

[9] C. Jiang; Z. Wang Strongly Irreducible Operators on Hilbert Space, Pitman Research Notes in Mathematics Series, vol. 389, Longman, Harlow, 1998 (x+243 pp)

[10] A. Koranyi; G. Misra A classification of homogeneous operators in the Cowen–Douglas class, Adv. Math., Volume 226 (2011), pp. 5338-5360

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