Multipliers and operator algebras on bounded analytic functions

Martin Bartelt

Vol. 37 (1971), No. 3, 575–584

DOI: 10.2140/pjm.1971.37.575

Abstract

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 c_n, we have T(∑ a_nzⁿ) = ∑ a_nc_nzⁿ for any function ∑ a_nzⁿ in B. We characterize all the multipliers from B into B and study their continuity properties.

Mathematical Subject Classification 2000

Primary: 47B99

Secondary: 46E15

Milestones

Received: 6 May 1970

Published: 1 June 1971