Approximation numbers of composition operators on H p
Daniel Li ; Hervé Queffélec ; Luis Rodríguez-Piazza
Concrete Operators, Tome 2 (2015), / Harvested from The Polish Digital Mathematics Library

give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:270832
@article{bwmeta1.element.doi-10_1515_conop-2015-0005,
     author = {Daniel Li and Herv\'e Queff\'elec and Luis Rodr\'\i guez-Piazza},
     title = {
      Approximation numbers of composition operators on H
      p
    },
     journal = {Concrete Operators},
     volume = {2},
     year = {2015},
     zbl = {06477135},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0005}
}
Daniel Li; Hervé Queffélec; Luis Rodríguez-Piazza. 
      Approximation numbers of composition operators on H
      p
    . Concrete Operators, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0005/

[1] B. Carl, A. Hinrichs, Optimal Weyl-type inequalities for operators in Banach spaces, Positivity 11 (2007), 41–55. | Zbl 1123.47019

[2] B. Carl, I. Stephani, Entropy, Compactness and the Approximation of Operators, Cambridge Tracts in Mathematics, Vol. 98 (1990). | Zbl 0705.47017

[3] B. Carl, H. Triebel, Inequalities between eigenvalues, entropy numbers, and related quantities of compact operators in Banach spaces, Math. Ann. 251 (1980), 129–133. | Zbl 0465.47019

[4] P. L. Duren, Theory of Hp Spaces, Dover Public. (2000).

[5] J. Garnett, Bounded Analytic Functions, revised first edition, Graduate Texts in Mathematics 236, Springer-Verlag (2007).

[6] K. Hoffman, Banach Spaces of Analytic Functions, revised first edition, Prentice-Hall (1962).

[7] C. V. Hutton, On the approximation numbers of an operator and its adjoint, Math. Ann. 210 (1974), 277–280. | Zbl 0272.47017

[8] P. Lefèvre, D. Li, H. Queffélec, L. Rodríguez-Piazza, Some new properties of composition operators associated to lensmaps, Israel J. Math. 195 (2) (2013), 801–824. | Zbl 1318.47039

[9] D. Li and H. Queffélec, Introduction à l’étude des espaces de Banach. Analyse et probabilités, Cours Spécialisés 12, Société Mathématique de France, Paris (2004).

[10] D. Li, H. Queffélec, L. Rodríguez-Piazza, On approximation numbers of composition operators, J. Approx. Theory 164 (4) (2012), 431–459. | Zbl 1246.47007

[11] D. Li, H. Queffélec, L. Rodríguez-Piazza, Estimates for approximation numbers of some classes of composition operators on the Hardy space, Ann. Acad. Sci. Fenn. Math. 38 (2013), 547–564. | Zbl 1295.47011

[12] D. Li, H. Queffélec, L. Rodríguez-Piazza, A spectral radius type formula for approximation numbers of composition operators, J. Funct. Anal., 267 (2014), no. 12, 4753–4774. | Zbl 1325.47045

[13] R. Mortini, Thin interpolating sequences in the disk, Arch. Math. 92, no. 5 (2009), 504–518. | Zbl 1179.30058

[14] N. Nikol’skiˇı, A treatise on the Shift Operator, Grundlehren der Math. 273, Springer-Verlag (1986).

[15] S. Petermichl, S. Treil, B.D. Wick, Carleson potentials and the reproducing kernel thesis for embedding theorems, Illinois J. Math. 51, no. 4 (2007), 1249–1263. | Zbl 1152.30036

[16] A. Pietsch, s-numbers of operators in Banach spaces, Studia Math. LI (1974), 201–223. | Zbl 0294.47018

[17] A. Plichko, Rate of decay of the Bernstein numbers, Zh. Mat. Fiz. Anal. Geom. 9, no. 1 (2013), 59–72. | Zbl 1294.47030

[18] H. Queffélec, K. Seip, Decay rates for approximation numbers of composition operators, J. Anal. Math., 125 (2015), no. 1, 371–399. | Zbl 1316.47022