Definition:Spectrum of Banach Algebra

Definition

Let $\struct {A, \norm {\, \cdot \,} }$ be a Banach algebra over $\C$.

Let $\Phi_A$ be the set of characters on $A$.

We call $\Phi_A$ the spectrum of $A$.

Sources

• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $4.10$: The continuity of characters