Category:Spectrum of Element in Unital Subalgebra

This category contains pages concerning Spectrum of Element in Unital Subalgebra:

Let $A$ be a unital algebra over $\C$.

Let $B$ be a unital subalgebra of $A$.

Let $x \in B$.

Let $\map {\sigma_A} x$ and $\map {\sigma_B} x$ be the spectra of $x$ in $A$ and $B$ respectively.

Then:

$\map {\sigma_A} x \subseteq \map {\sigma_B} x$