On the commutant of certain multiplication operators on spaces of analytic functions |
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Authors: | B. Khani Robati |
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Affiliation: | (1) Department of Mathematics College of Sciences, Shiraz University, 71454 Shiraz, Iran |
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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. Research supported by the Shiraz University Grant 78-SC-1188-657. |
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Keywords: | KeywordHeading" >AMS Subject Classifications Primary 47B35 Secondary 47B38 |
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