Definition:Modulus of Element of C*-Algebra

Definition

Let $\struct {A, \ast, \norm {\, \cdot \,} }$ be a $\text C^\ast$-algebra.

Let $a \in A$.

From Product of Element of C*-Algebra with its Star is Positive, $a^\ast a$ is positive.

Hence we can consider the square root $\paren {a^\ast a}^{1/2}$.

We define the modulus $\cmod a$ of $a$ by:

$\cmod a = \paren {a^\ast a}^{1/2}$

Although this article appears correct, it's inelegant. There has to be a better way of doing it. In particular: Extract the justification to a separate section You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by redesigning it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Improve}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1990: Gerard J. Murphy: C*-Algebras and Operator Theory ... (previous) ... (next): $2.2$: Positive Elements of $C^\ast$-Algebras