Definition 33.1.3 (Homomorphism).label Let $A, B$ be Banach algebras and $\phi: A \to B$, then $\phi$ is a homomorphism if:
- (1)
$\phi \in L(A; B)$.
- (2)
For each $x, y \in A$, $\phi(xy) = \phi(x)\phi(y)$.
Definition 33.1.3 (Homomorphism).label Let $A, B$ be Banach algebras and $\phi: A \to B$, then $\phi$ is a homomorphism if:
$\phi \in L(A; B)$.
For each $x, y \in A$, $\phi(xy) = \phi(x)\phi(y)$.
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