Vol. 22, No. 3, 1967

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Multipliers and H∗ algebras

Wai-Mee Ching and James Sai-Wing Wong

Vol. 22 (1967), No. 3, 387–395

Let A be a normed algebra and B(A) the algebra of all bounded linear operators from A into itself, with operator norm. An element T B(A) is called a multiplier of A if (Tx)y = x(Ty) for all x,y A. The set of all multipliers of A is denoted by M(A). In the present paper, it is first shown that M(A) is a maximal commutative subalgebra of B(A) if and only if A is commutative. Next, M(A) in case A is an H-algebra wi# l be represented as the algebra of all complexvalued functions on certain discrete space. Finally, as an application of the representation theorem of M(A), the set of all compact multipliers of compact H-algebras is characterized.

Mathematical Subject Classification
Primary: 46.60
Received: 7 June 1966
Published: 1 September 1967
Wai-Mee Ching
James Sai-Wing Wong