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2008-10-19 19:28:34
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Version 7 --> Version 8
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bci1
| self-adjoint elements in a \PMlinkname{$C^*$-algebra}{CAlgebra} that we will now describe. Let $\mathcal{A}$ be a $C^*$-algebra with identity element $e$, and then recall that an element $a \in \mathcal{A}$ is {\em self-adjoint} if $a^* = a$. Let us also recall that every element $a$ in a $C^*$-algebra has a |
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2008-10-19 19:25:51
- revision [
Version 6 --> Version 7
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by
bci1
Let $\mathcal{A}$ be a $C^*$-algebra with identity element $e$,and then recall that an element $a \in \mathcal{A}$ is {\em self-adjoint} if $a^* = a$. Let us also recall that every element $a$ in a $C^*$-algebra has a unique decomposition of the form
\begin{displaymath}
a = x + i y ,
\end{displaymath}
where $x, y$ are self-adjoint elements; ``moreover, every self-adjoint element $a$ is of the form
\begin{displaymath}
a = x - y
\end{displaymath}
where $x, y$ are positive elements''.
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