Equation 19 · Part 2 · The Entry a Relabeling Cannot Write

Symbol I_c

\Lambda^\dagger(I_c) = I_f

I_c

What this part means

$I_c$ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Its job in the formula

$I_c$ is an argument of the function-like quantity on the left; its role is set by that function’s stated inputs.

Full expressionSymbol I_cArticle meaning

The passage around this formula

$\Lambda^\dagger$ is positive because $\Lambda$ is completely positive and every $\Lambda(\rho)$ with $\rho$ $\ge$ 0 is itself a valid state; it is unital, $\Lambda^\dagger(I_c)$ = $I_f$ , because $\Lambda$ preserves trace for every input. This duality is the same construction Stinespring used to show that any completely positive map admits a dilation to a larger, unitary description [ 9 ] , and it lets a coarse Hamiltonian be pulled back onto the fine space without the fine space’s own structure ever being disturbed.

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[9] Positive Functions on C*-Algebras ↗

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