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Banach star algebra
A Banach \(\ast\text{-algebra}\) \(A\) is a multiplicative involutive Banach space whose norm satisfies the following: \[ \left\| ab \right\| \leq \left\| a \right\|\left\| b \right\| \] for all \(a,b \in A\).
Maps
\(\ast\text{-homomorphism}\)
A multiplicative, linear, \(\ast\text{-preserving}\) map between Banach \(\ast\text{-algebras}\) is called a \(\ast\text{-homomorphism}\).
\(\ast\text{-isomorphism}\)
A bijective \(\ast\text{-homomorphism}\) is a \(\ast\text{-isomorphism}\).
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