Abstract
Some conditions which are equivalent to finite dimensionality for a semi-simple Banach algebra A are given, and simplification of the proofs of previously known results are included. These conditions include local finiteness, spectral finiteness and the condition that socle A exists and is equal to A.
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Al-Moajil, A.H. Characterization of finite dimensionality for semi-simple Banach algebras. Manuscripta Math 33, 315–325 (1981). https://doi.org/10.1007/BF01798230
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DOI: https://doi.org/10.1007/BF01798230