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Definition: Möbius elements

Operator-valued Möbius hierarchy and three orders · lines 1587–1597

En01-A@1#def:mobius

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For $J \subseteq N$ , define

Z_{J} = K \subseteq J \sum (- 1)^{∣ J ∣ - ∣ K ∣} Δ_{K} ρ, ω_{J} (Λ) = \frac{1}{2} ∥Λ (Z_{J}) ∥_{1}, η_{M} (J) = tr (M Z_{J}) .

One has $Z_{\emptyset} = ρ$ , and $Z_{J}$ is traceless for nonempty $J$ .

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unlabeled · line 1589
$Z_{J} = K \subseteq J \sum (- 1)^{∣ J ∣ - ∣ K ∣} Δ_{K} ρ, ω_{J} (Λ) = \frac{1}{2} ∥Λ (Z_{J}) ∥_{1}, η_{M} (J) = tr (M Z_{J}) .$

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