Manuscript En05-C@1 · En05-C.tex · section · aa213ea6

Stage A: the tensor-free comparison theorem

Stage A: the tensor-free comparison theorem · lines 368–381

We use the standard Jordan decomposition of a bounded Hermitian functional:

f = f_{+} - f_{-}, f_{\pm} \geq 0, ∥ f ∥ = f_{+} (1) + f_{-} (1) .

In a von Neumann algebra, the decomposition of a normal Hermitian functional is normal. These are background functional-analysis facts Pedersen,Sakai.

Displayed formulas in this passage

unlabeled · line 373
$f = f_{+} - f_{-}, f_{\pm} \geq 0, ∥ f ∥ = f_{+} (1) + f_{-} (1) .$

Nearby in this section

lemma: Lemma: Separation by equal-snapshot states
theorem: Theorem: Tensor-free snapshot–channel–adjoint equivalence
remark: Remark: The local channel is not a homomorphism
corollary: Corollary: Recovery of the supplied hybrid comparison
remark: Remark: Restriction versus extension