Vol. 37, No. 3, 1971

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Multipliers and operator algebras on bounded analytic functions

Martin Bartelt

Vol. 37 (1971), No. 3, 575–584

Let B denote the vector space of bounded analytic functions on the open unit disc. The first part of this paper involves the use of three topologies on B which give rise to various continuity classes of operators from B to B, and the study of the relationships among these classes. The second is the examination of a special class of operators called multipliers. An operator T is a multiplier if for some sequence cn, we have T( anzn) = ancnzn for any function anzn in B. We characterize all the multipliers from B into B and study their continuity properties.

Mathematical Subject Classification 2000
Primary: 47B99
Secondary: 46E15
Received: 6 May 1970
Published: 1 June 1971
Martin Bartelt