Commutants of certain multiplication operators on Hilbert spaces of analytic functions

K. Seddighi; S. Vaezpour

Studia Mathematica (1999)

  • Volume: 133, Issue: 2, page 121-130
  • ISSN: 0039-3223

Abstract

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This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let A = M z be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with A n for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.

How to cite

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Seddighi, K., and Vaezpour, S.. "Commutants of certain multiplication operators on Hilbert spaces of analytic functions." Studia Mathematica 133.2 (1999): 121-130. <http://eudml.org/doc/216608>.

@article{Seddighi1999,
abstract = {This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let $A=M_z$ be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with $A^n$ for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.},
author = {Seddighi, K., Vaezpour, S.},
journal = {Studia Mathematica},
keywords = {commutant; multiplication operators; Hilbert spaces of analytic functions; reproducing kernel},
language = {eng},
number = {2},
pages = {121-130},
title = {Commutants of certain multiplication operators on Hilbert spaces of analytic functions},
url = {http://eudml.org/doc/216608},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Seddighi, K.
AU - Vaezpour, S.
TI - Commutants of certain multiplication operators on Hilbert spaces of analytic functions
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 2
SP - 121
EP - 130
AB - This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let $A=M_z$ be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with $A^n$ for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.
LA - eng
KW - commutant; multiplication operators; Hilbert spaces of analytic functions; reproducing kernel
UR - http://eudml.org/doc/216608
ER -

References

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  1. [1] G. T. Adams, P. J. McGuire and V. I. Paulsen, Analytic reproducing kernels and multiplication operators, Illinois J. Math. 36 (1992), 404-419. Zbl0760.47010
  2. [2] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337-404. Zbl0037.20701
  3. [3] J. B. Conway, The Theory of Subnormal Operators, Math. Surveys Monographs 36, Amer. Math. Soc., 1991. Zbl0743.47012
  4. [4] Ž. Čučković, Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), 277-285. Zbl0802.47018
  5. [5] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972. Zbl0247.47001
  6. [6] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. Zbl0469.30024
  7. [7] R. Gellar, Operators commuting with a weighted shift, preprint. Zbl0189.13403
  8. [8] S. Power, The Cholesky decomposition in Hilbert space, Inst. Math. Appl. Conf. Ser. 22 (1986), 186-187. Zbl0645.47013
  9. [9] K. Seddighi, Operators acting on Hilbert spaces of analytic functions, a series of lectures, Dept. of Math., Univ. of Calgary, Alberta, 1991. 
  10. [10] A. L. Shields and L. J. Wallen, The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788. Zbl0207.13801
  11. [11] K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990. Zbl0706.47019

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