Spectral permanence for C-star algebras
= Spectral permanence for C-star algebras
{title2=$\sigma_A(a)=\sigma_B(a)$}
If $A$ is a closed <C-star algebra> inside a unital <C-star algebra> $B$ and the two algebras share their identity, an element of $A$ is invertible in $A$ exactly when it is invertible in $B$. Consequently its <spectrum of an element> does not depend on which of these two algebras is used.