# Commutants of certain multiplication operators on Hilbert spaces of analytic functions

Studia Mathematica (1999)

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

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topSeddighi, 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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- [6] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981. Zbl0469.30024
- [7] R. Gellar, Operators commuting with a weighted shift, preprint. Zbl0189.13403
- [8] S. Power, The Cholesky decomposition in Hilbert space, Inst. Math. Appl. Conf. Ser. 22 (1986), 186-187. Zbl0645.47013
- [9] K. Seddighi, Operators acting on Hilbert spaces of analytic functions, a series of lectures, Dept. of Math., Univ. of Calgary, Alberta, 1991.
- [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] K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990. Zbl0706.47019

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