  Let $ A$ be a complex unital Banach algebra. An element $a \in A$ is said to
be Hermitian, if $ \| \exp (ita) \| =1$ for all $t\in R$. In the case of the
algebra of bounded linear operators in a Hilbert space this Hermitian property
agrees with the ordinary selfadjointness. If $a \in A$ is Hermitian, then
$|a|=||a||$, where $|a|$ denotes the spectral radius of $a$. A function $F:
R\to \C$ is called the universal symbol if $ \|| F(a)||= |F(a)|$\ for each $ A$
and all Hermitian $a\in A$. We characterize universal symbols in terms of
positive definite functions.
