= Quasinilpotent element
{title2=$\rho(x)=0$}
An element of a complex unital <Banach algebra> is quasinilpotent if its <spectral radius> is zero, equivalently its <spectrum of an element> is $\{0\}$. A <nilpotent element> is quasinilpotent, but the converse need not hold. The <Volterra convolution algebra on a finite interval> gives powers which never vanish, yet have factorially decreasing norms, making the inverse series for $\lambda e-x$ converge for every $\lambda\ne0$.
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