Category:Spectrum of Element of Unital Commutative Banach Algebra

This category contains pages concerning Spectrum of Element of Unital Commutative Banach Algebra:

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

Let $\Phi_A$ be the spectrum of $A$.

Let $x \in A$.

Let $\map {\sigma_A} x$ be the spectrum of $x$.

Then:

$\map {\sigma_A} x = \set {\map \phi x : \phi \in \Phi_A}$