Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

Let $A$ be a Banach $^*$-algebra with an identity, continuous involution, center $Z$ and set of self-adjoint elements ${\mit\Sigma}$. Let $h\in{\mit\Sigma}$. The set of $v\in{\mit\Sigma}$ such that $(h+iv)^n$ is normal for no positive integer $n$ is dense in ${\mit\Sigma}$ if and only if $h\not\in Z$. The case where $A$ has no identity is also treated.