Toeplitz operators in the commutant of a composition operator

Bruce Cload

Studia Mathematica (1999)

  • Volume: 133, Issue: 2, page 187-196
  • ISSN: 0039-3223

Abstract

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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 ∘ ϕ . In this article, we consider which Toeplitz operators T f satisfy T f C ϕ = C ϕ T f

How to cite

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Cload, Bruce. "Toeplitz operators in the commutant of a composition operator." Studia Mathematica 133.2 (1999): 187-196. <http://eudml.org/doc/216613>.

@article{Cload1999,
abstract = {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 $C_ϕ(f) = f∘ϕ$. In this article, we consider which Toeplitz operators $T_f$ satisfy $T_\{f\}C_\{ϕ\} = C_\{ϕ\}T_\{f\}$},
author = {Cload, Bruce},
journal = {Studia Mathematica},
keywords = {Hardy-Hilbert space; composition operator; Toeplitz operators},
language = {eng},
number = {2},
pages = {187-196},
title = {Toeplitz operators in the commutant of a composition operator},
url = {http://eudml.org/doc/216613},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Cload, Bruce
TI - Toeplitz operators in the commutant of a composition operator
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 2
SP - 187
EP - 196
AB - 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 $C_ϕ(f) = f∘ϕ$. In this article, we consider which Toeplitz operators $T_f$ satisfy $T_{f}C_{ϕ} = C_{ϕ}T_{f}$
LA - eng
KW - Hardy-Hilbert space; composition operator; Toeplitz operators
UR - http://eudml.org/doc/216613
ER -

References

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  3. [3] B. Cload, Generating the commutant of a composition operator, in: Contemp. Math. 213, Amer. Math. Soc., 1998, 11-15. Zbl0901.47017
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  11. [11] K. Hoffman, Banach Spaces of Analytic Functions, Dover, 1988. Zbl0734.46033
  12. [12] P. Hurst, A model for the invertible composition operators on H 2 , Proc. Amer. Math. Soc. 124 (1996), 1847-1856. Zbl0857.47017
  13. [13] E. A. Nordgren, Composition operators, Canad. J. Math. 20 (1968), 442-449. Zbl0161.34703
  14. [14] E. A. Nordgren, P. Rosenthal and F. S. Wintrobe, Invertible composition operators on H p , J. Funct. Anal. 73 (1987), 324-344. 
  15. [15] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1987. Zbl0925.00005
  16. [16] J. H. Shapiro, Composition Operators and Classical Function Theory, Springer, New York, 1993. Zbl0791.30033
  17. [17] A. L. Shields, On fixed points of commuting analytic functions, Proc. Amer. Math. Soc. 15 (1964), 703-706. Zbl0129.29104
  18. [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. 

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