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Homomorphisms of
annihilator Banach algebras. II
Gregory Frank Bachelis |
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Vol. 30 (1969), No. 2, 283–291
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Abstract |
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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)∥≦ K∥x∥⋅∥y∥ whenever 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
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Milestones
Received: 17 January 1969
Published: 1 August 1969
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Authors |
| Gregory Frank Bachelis | |
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