Vol. 30, No. 2, 1969

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ISSN: 0030-8730
Homomorphisms of annihilator Banach algebras. II

Gregory Frank Bachelis

Vol. 30 (1969), No. 2, 283–291

Let A be a semi-simple annihilator Banach algebra, and let ν be a homomorphism of A into a Banach algebra. In this paper it is shown that there exists a constant K and dense two-sided ideals containing the socle, IL and IR, such that ν(xy)Kx∥⋅∥ywhenever x IL or y IR. If A has a bounded left or right approximate identity, then ν is continuous on the socle. Thus if A = L1(G), where G is a compact topological group, then any homomorphism of A into a Banach algebra is continuous on the trigonometric polynomials.

Mathematical Subject Classification
Primary: 46.50
Received: 17 January 1969
Published: 1 August 1969
Gregory Frank Bachelis