Equation 12 · The Entry a Relabeling Cannot Write

What does this equation mean?

\Lambda^\dagger: \mathcal B(\mathcal H_c) \to \mathcal B(\mathcal H_f)

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This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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\Lambda^\dagger

Symbol Lambda^dagger

the define.

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B

Symbol B

B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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H_c

Symbol H_c

wrong, does not touch the total energy of any closed system, and does not by itself explain where a nonzero reading comes from.

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H_f

Symbol H_f

$H_f$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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How to interpret it

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What the article says around this equation

Every channel has a dual. Define $\Lambda^\dagger$ : $\mathcal B(\mathcal H_c)$ $\to$ $\mathcal B(\mathcal H_f)$ by the pairing that must hold for every fine state and every coarse observable $O_c$ ,

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Sources cited in the article section

[9] Positive Functions on C*-Algebras ↗

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