Comptes Rendus
no. 2
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

Crispin Herrera Yañez1 ; Ondrej Hutník2 ; Egor A. Maximenko3
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, Volume 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
Crispin Herrera Yañez 1 ; Ondrej Hutník 2 ; Egor A. Maximenko 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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     title = {Vertical symbols, {Toeplitz} operators on weighted {Bergman} spaces over the upper half-plane and very slowly oscillating functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {129--132},
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Crispin Herrera Yañez; Ondrej Hutník; Egor A. Maximenko. Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 129-132. doi : 10.1016/j.crma.2013.12.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.004/

[1] S. Grudsky; A. Karapetyants; N. Vasilevski Dynamics of properties of Toeplitz operators on the upper half-plane: Parabolic case, J. Oper. Theory, Volume 52 (2004), pp. 185-204

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

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

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

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

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

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