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If $ A$ is a Banach algebra and $ a \in A$ is an idempotent, it is well known that $ \sigma(a) = \{0; 1\}$ . Is the converse true ?, ie if $ \sigma (a) = \{0; 1\}$ does it mean that $ a$ is an idempotent ?Read more

A semigroup presentation $ \langle A | R\rangle$ is called a tree-like if every relation has the form $ ab=c$ , $ a,b,c$ are in $ A$ and if two relations $ ab=c, a’b’=c’$ belong to $ R$ , then $ c=c’$ if and only if $ a=a’$ and $ b=b’$ . Example: $ P=\langleRead more