Toeplitz operators in the commutant of a composition operator

Cload, Bruce

Cload, Bruce

Studia Mathematica, Tome 133 (1999), p. 187-196 / Harvested from The Polish Digital Mathematics Library

Résumé

If ϕ is an analytic self-mapping of the unit disc D and if $H^{2} (D)$ is the Hardy-Hilbert space on D, the composition operator $C_{ϕ}$ on $H^{2} (D)$ is defined by $C_{ϕ} (f) = f \circ ϕ$ . In this article, we consider which Toeplitz operators $T_{f}$ satisfy $T_{f} C_{ϕ} = C_{ϕ} T_{f}$

Publié le : 1999-01-01

Zbl 0924.47017

EUDML-ID : urn:eudml:doc:216613

@article{bwmeta1.element.bwnjournal-article-smv133i2p187bwm,
     author = {Bruce Cload},
     title = {Toeplitz operators in the commutant of a composition operator},
     journal = {Studia Mathematica},
     volume = {133},
     year = {1999},
     pages = {187-196},
     zbl = {0924.47017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv133i2p187bwm}
}

Cload, Bruce. Toeplitz operators in the commutant of a composition operator. Studia Mathematica, Tome 133 (1999) pp. 187-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv133i2p187bwm/

Bibliographie

[00000] [1] D. F. Behan, Commuting analytic functions without fixed points, Proc. Amer. Math. Soc. 37 (1973), 114-120. | Zbl 0251.30009

[00001] [2] R. B. Burckel, Iterating analytic self-maps of discs, Amer. Math. Monthly 88 (1981), 396-407. | Zbl 0466.30001

[00002] [3] B. Cload, Generating the commutant of a composition operator, in: Contemp. Math. 213, Amer. Math. Soc., 1998, 11-15. | Zbl 0901.47017

[00003] [4] B. Cload, Composition operators: hyperinvariant subspaces quasi-normals and isometries, Proc. Amer. Math. Soc., to appear. | Zbl 0917.47027

[00004] [5] C. C. Cowen, The commutant of an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978), 1-31. | Zbl 0391.47014

[00005] [6] C. C. Cowen, Commuting analytic functions, ibid. 265 (1981), 69-95.

[00006] [7] C. C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, 1995. | Zbl 0873.47017

[00007] [8] C. C. Cowen and B. MacCluer, Some problems on composition operators, in: Contemp. Math. 213, Amer. Math. Soc., 1998, 17-25.

[00008] [9] P. Duren, Theory of $H^{p}$ Spaces, Academic Press, 1970.

[00009] [10] M. H. Heins, A generalization of the Aumann-Carathéodory "Starrheitssatz", Duke Math. J. 8 (1941), 312-316. | Zbl 67.0283.02

[00010] [11] K. Hoffman, Banach Spaces of Analytic Functions, Dover, 1988. | Zbl 0734.46033

[00011] [12] P. Hurst, A model for the invertible composition operators on $H^{2}$ , Proc. Amer. Math. Soc. 124 (1996), 1847-1856. | Zbl 0857.47017

[00012] [13] E. A. Nordgren, Composition operators, Canad. J. Math. 20 (1968), 442-449. | Zbl 0161.34703

[00013] [14] E. A. Nordgren, P. Rosenthal and F. S. Wintrobe, Invertible composition operators on $H^{p}$ , J. Funct. Anal. 73 (1987), 324-344.

[00014] [15] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987. | Zbl 0925.00005

[00015] [16] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer, New York, 1993. | Zbl 0791.30033

[00016] [17] A. L. Shields, On fixed points of commuting analytic functions, Proc. Amer. Math. Soc. 15 (1964), 703-706. | Zbl 0129.29104

[00017] [18] A. L. Shields and L. J. Wallen, The commutants of certain Hilbert space operators, in: Indiana Univ. Math. Surveys 13, Amer. Math. Soc., Providence, 1974, 49-128.