Functional analysis
Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions
[Les symboles verticaux, opérateurs de Toeplitz sur les espaces pondérés de Bergman sur le demi-plan supérieur et fonctions à oscillation très lente]

Présenté par : the Editorial Board

Herrera Yañez, Crispin1 ; Hutník, Ondrej2 ; Maximenko, Egor A.3
1 Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, 07000, D.F. México, Mexico
2 Institute of Mathematics, Faculty of Science, P. J. Šafárik University in Košice, Jesenná 5, 040 01 Košice, Slovakia
3 Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07730, D.F. México, Mexico
Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 129-132.

En étendant le résultat récent de Herrera Yañez, Maximenko et Vasilevski, nous allons proposer une nouvelle étape dans lʼanalyse structurelle des algèbres générées par les opérateurs de Toeplitz agissant sur les espaces pondérés de Bergman sur le demi-plan supérieur. Nous allons montrer que lʼensemble des fonctions « spectrales » correspondant aux opérateurs de Toeplitz à symboles bornés verticaux est dense dans la C⁎-algèbre des fonctions à oscillation très lente sur la demi-droite positive.

Extending a recent result of Herrera Yañez, Maximenko and Vasilevski, we provide a further step in the structural analysis of algebras generated by Toeplitz operators on weighted Bergman spaces over the upper half-plane. We show that the set of “spectral” functions corresponding to Toeplitz operators generated by bounded vertical symbols is dense in the C⁎-algebra of very slowly oscillating functions on the positive half-line.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.12.004
Herrera Yañez, Crispin 1 ; Hutník, Ondrej 2 ; Maximenko, Egor A. 3

1 Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, 07000, D.F. México, Mexico
2 Institute of Mathematics, Faculty of Science, P. J. Šafárik University in Košice, Jesenná 5, 040 01 Košice, Slovakia
3 Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07730, D.F. México, Mexico 
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     journal = {Comptes Rendus. Math\'ematique},
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Herrera Yañez, Crispin; Hutník, Ondrej; Maximenko, Egor A. Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions. Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 129-132. doi : 10.1016/j.crma.2013.12.004. https://www.numdam.org/articles/10.1016/j.crma.2013.12.004/

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[2] Herrera Yañez, C.; Maximenko, E.A.; Vasilevski, N.L. Vertical Toeplitz operators on the upper half-plane and very slowly oscillating functions, Integral Equ. Oper. Theory, Volume 77 (2013), pp. 149-166

[3] Hutník, O.; Hutníková, M. Toeplitz operators on poly-analytic spaces via time-scale analysis, Oper. Matrices (2013) (in press)

[4] Suárez, D. The eigenvalues of limits of radial Toeplitz operators, Bull. Lond. Math. Soc., Volume 40 (2008), pp. 631-641

[5] Vasilevski, N.L. On Bergman–Toeplitz operators with commutative symbol algebras, Integral Equ. Oper. Theory, Volume 34 (1999), pp. 107-126

[6] Vasilevski, N.L. Commutative Algebras of Toeplitz Operators on the Bergman Space, Operator Theory: Advances and Applications, vol. 185, Birkhäuser, Basel, 2008

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