To prove the famous Cohen factorization theorem, even in Banach algebras, having a bounded approximate identity has special importance. In extending the Cohen’s theorem to topological algebras, we not only use an approximate identity, but some more powerful boundedness is also needed. Here we recall an open problem about uniformly bounded approximate identities on complete metrizable LMC algebras, and try to answer it1.

Keywords: extending the Cohen’s theorem to topological algebras, we not only use an approximate identity

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