Relations To Other Results
This result is related to the Von Neumann bicommutant theorem, which states that, for a *-algebra A of operators on a Hilbert space H, the double commutant A′′ can be approximated by A on any given finite set of vectors. See also the Kaplansky density theorem in the von Neumann algebra setting.
Read more about this topic: Jacobson Density Theorem
Famous quotes containing the words relations and/or results:
“Actually, the laboring man has not leisure for a true integrity day by day; he cannot afford to sustain the manliest relations to men; his labor would be depreciated in the market.
He has no time to be anything but a machine.”
—Henry David Thoreau (1817–1862)
“Different persons growing up in the same language are like different bushes trimmed and trained to take the shape of identical elephants. The anatomical details of twigs and branches will fulfill the elephantine form differently from bush to bush, but the overall outward results are alike.”
—Willard Van Orman Quine (b. 1908)