Operator Algebra
Note 4
Frame Operator
TANAKA Akio
1
Hilbert space H
Sequence of points in H {xn}
Certain constants 0 < A ≦ B < ∞
x ∈ H
A ||x||2 ≦∑n |<x, xn>|2 ≦ B ||x||2
{xn} is frame.
A is lower bound.
B is upper bound.
2
x ∈ H
∑n <x, xn>||xn|| is convergent.
S : x ↦ ∑n <x, xn>xn satisfies A ≦S≦ B.
S is frame operator.
[References]
Frame / Tokyo February 27, 2005
More details, Quantum Theory for Language Map 1
Frame-Quantum Theory / Tokyo March 12, 2005
More details, Frame-Quantum Theory Map 2
Tokyo April 2, 2008
Sekinan Research Field of Language
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