Note 1
Measure
1
locally compact space Ω
compact subset of Ω K
continuous complex valued function space K (Ω)
linear functional over K (Ω) μ
positive number λ
f ∈K (Ω)
| μ (f) | ≦ λ supω∈Ω | f (ω)|
μ is measure over Ω.
2
sequence of points {xn}, {yn} ⊂ H
∑n || xn ||2 < ∞
∑n || yn ||2 < ∞
3
Hilbert space H
bounded operator from H to K B (H, K )
B ( H ) : = B ( H, H )
sub-algebra that is self-adjoint set *sub-algebra
*sub-algebra of B ( H ) that contains identity operator I and is closed by ultra weak topology (τuw)
*sub-algebra of B ( H ) N
linear functional A∈N ↦ ∑n < xn, Ayn> is τuw-continuous.
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