Category:Spectrum of Element of Banach Algebra is Bounded

This category contains pages concerning Spectrum of Element of Banach Algebra is Bounded:

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

Let $x \in A$.

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

Then $\map {\sigma_A} x$ is bounded, and in particular:

$\cmod \lambda \le \norm x$ for all $\lambda \in \map {\sigma_A} x$