Notes about math, research, and more.

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 \(\ast\text{-isomorphism}\).