I know that every C*-algebra has an approximate unit. I have two questions: why we cannot show that every involutive Banach algebra has an approximate unit? I need an example of an involutive Banach algebra which does not have any approximate unit. Thanks in advance.
2026-03-27 04:38:43.1774586323
Approximate unit of an involutive Banach algebra
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The simplest example would be a nonzero algebra with any involution and zero multiplication.