Commutants of certain multiplication operators on Hilbert spaces of analytic functions

• Autorzy: K. Seddighi , S. M. Vaezpour
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

commutant   multiplication operators   Hilbert spaces of analytic functions   reproducing kernel  

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 2
• Strony: 121-130

Daty

wydano

1999

otrzymano

1997-03-24

poprawiono

1998-07-09

poprawiono

1998-10-11

Twórcy

autor

K. Seddighi

• Department of Mathematics, Shiraz University, 71454 Shiraz, Iran ,

autor

S. M. Vaezpour

• 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.