• COMMUTANT OF THE DIRECT SUM OF MULTIPLICATION OPERATORS

K. Hedayatian*

Abstract


For, suppose that is Banach space of analytic functions on a bounded domain in the complex plane, and  for . Let  denote the operator of multiplication by  on . It is shown that the commutatnt and the double commutatnt of  are equal; furthermore, the commutant of  split. That is, . Also, we prove that the direct sum of an upper or lower triangular operator on  and another one on  split.


Keywords


Commutant, Direct sum, Multiplication operators.

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