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:
“As death, when we come to consider it closely, is the true goal of our existence, I have formed during the last few years such close relations with this best and truest friend of mankind, that his image is not only no longer terrifying to me, but is indeed very soothing and consoling! And I thank my God for graciously granting me the opportunity ... of learning that death is the key which unlocks the door to our true happiness.”
—Wolfgang Amadeus Mozart (1756–1791)
“Nothing is as difficult as to achieve results in this world if one is filled full of great tolerance and the milk of human kindness. The person who achieves must generally be a one-ideaed individual, concentrated entirely on that one idea, and ruthless in his aspect toward other men and other ideas.”
—Corinne Roosevelt Robinson (1861–1933)