Let $A$ be a unital commutative Banach algebra.What can be the consequences of the spectral radius of an element $a$ equaling its norm $\|a\|$.
2026-03-26 12:46:55.1774529215
Uses of spectral radius equal to norm.
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I can't think of any interesting consequences offhand.
Now, assuming that the spectral radius of every element of $A$ is equal to the norm does have an interesting consequence - in fact it's easy to see that that condition is equivalent to saying $A$ is isometrically isomorphic to a closed subalgebra of $C(K)$ for some compact Hausdorff space $K$.