Vol. 41, No. 2, 1972

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Homomorphisms of Banach algebras with minimal ideals

Gregory Frank Bachelis

Vol. 41 (1972), No. 2, 307–311

Let A be a semi-simple Banach algebra with socle F, and let ν be a homomorphism of A into a Banach algebra. It is shown that if I is a minimal one-sided ideal of A, then the restriction of v to I is continuous. This is then used to deduce continuity properties of the restriction of ν to F. In particular, if F has a bounded left or right approximate identity, then ν is continuous on F.

Mathematical Subject Classification 2000
Primary: 46H05
Received: 20 May 1971
Published: 1 May 1972
Gregory Frank Bachelis