Abstract
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.
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Research supported by the Shiraz University Grant 78-SC-1188-657.
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Robati, B.K. On the commutant of certain multiplication operators on spaces of analytic functions. Rend. Circ. Mat. Palermo 49, 601–608 (2000). https://doi.org/10.1007/BF02904268
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DOI: https://doi.org/10.1007/BF02904268