Corollary 1

Let A be a star algebra and $x$ a normal element of A. Then $\|x\|=\varrho (x)$.

Since the star subalgebra of A generated by $x$ and $x^*$ is commutative, one may suppose that A is commutative. In this case, the cor. results from th. 1, from example 2 of I, p. 102 and from th. 1 of I, p. 24.