On the commutant of certain multiplication operators on spaces of analytic functions
Tóm tắt
Let ℬ be a Banach space of analytic functions defined on the open unit disk. We characterize the commutant ofM
Z
2 (the operator of multiplication by the square of independent variable defined on ℬ) and show that for an operatorS in the commutantM
Z
2 ifSM
Z
2k+1−M
Z
2k+1
S is compact for some nonnegative integerk, thenS=M
ϕ whereϕ is a multiplier of ℬ. Letn be a positive integer andS be an operator in the commutant ofM
Z
n defined on a functional Hilbert spaces of analytic functions. We show that under certain conditionsS has the formM
ϕ.
Tài liệu tham khảo
Axler S., Cuckovic Z.,Commuting Toeplitz operators with harmonic symbols. Integral Equation Operator Theory,14 (1991), 1–12.
Cuckovic Z.,Commutant of Toeplitz operators on the Bergman spaces, Pacific. J. Math.,162 (1994), 277–285.
Richter S.,Invariant subspaces in Banach spaces of analytic functions, Trans. Amer. Math. Soc.,304 (1987), 585–616.
Seddighi K., Vaespour S. M.,Commutant of certain multiplication operator on Hilbert spaces of analytic functions, Studia Math.,133 (2) (1999), 121–130.
Shields A. L., Wallen L. J.,The commutants of certain Hilbert space operators, Indiana Univ. Math. J.,20 (1971), 777–788.
Thomson J. E.,Intersections of commutants of analytic Toeplitz operators, Proc. Amer. Msath. Soc.,52 (1975), 305–310.
Thomson J. E.,The commutant of certain analytic Toeplitz operators, Proc. Amer. Math. Soc.,54 (1976), 165–169.