• COMMUTANT OF THE DIRECT SUM OF MULTIPLICATION OPERATORS

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.