Manuscript VII-G@1 · VII-G.tex · definition · 54f561e8

Definition: Observation space

Observation boundaries and stochastic histories › Observable linear spaces · lines 463–482

VII-G@1#eq:direct-observation

An observation space is a complex linear, adjoint-closed subspace $O \subseteq X_{G}$ containing $1$ . Thus it is a finite-dimensional operator system. It need not be closed under multiplication.

Two states agree on $O$ if

⟨ B, ρ ⟩ = ⟨ B, σ ⟩ (B \in O) .

A frequently used choice is

O_{A} = g ⨁ A_{g},

where each $A_{g} \subseteq L (H)$ is a unital $^{*}$ -subalgebra. This choice observes the complete classical label, because it contains each central block projection.

Displayed formulas in this passage

VII-G@1#eq:direct-observation · line 475
$O_{A} = g ⨁ A_{g},$
unlabeled · line 470
$⟨ B, ρ ⟩ = ⟨ B, σ ⟩ (B \in O) .$

Nearby in this section

section: Observable linear spaces
theorem: Theorem: Intrinsic hybrid observation criterion
section: Observable linear spaces