For $x$ a self adjoint element of a $C^*$ algebra it is equivalent:
- $x$ has non negative spectrum
- $x$ has a self adjoint square root $x=y^*y$x=y^2$
- $x$ is a finite sum of squares $x=\sum {a_i}^*a_i$
in this case $x$ is indeed called positive.
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For $x$ a self adjoint element of a $C^*$ algebra it is equivalent:
in this case $x$ is indeed called positive. |
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