Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
121-130
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-03-24
poprawiono
1998-07-09
poprawiono
1998-10-11
Twórcy
autor
- Department of Mathematics, Shiraz University, 71454 Shiraz, Iran, seddighi@sun01.susc.ac.ir
autor
- Department of Mathematics, Shiraz University, 71454 Shiraz, Iran
Bibliografia
- [1] G. T. Adams, P. J. McGuire and V. I. Paulsen, Analytic reproducing kernels and multiplication operators, Illinois J. Math. 36 (1992), 404-419.
- [2] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337-404.
- [3] J. B. Conway, The Theory of Subnormal Operators, Math. Surveys Monographs 36, Amer. Math. Soc., 1991.
- [4] Ž. Čučković, Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), 277-285.
- [5] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, New York, 1972.
- [6] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981.
- [7] R. Gellar, Operators commuting with a weighted shift, preprint.
- [8] S. Power, The Cholesky decomposition in Hilbert space, Inst. Math. Appl. Conf. Ser. 22 (1986), 186-187.
- [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.
- [11] K. Zhu, Operator Theory in Function Spaces, Marcel Dekker, New York, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv133i2p121bwm