nLab Francis J. Murray

• Wikipedia entry

Selected writings

Introducing the theory of what came to be known as von Neumann algebra factors:

The classification of factors into types I, II, III and the construction of examples not of type I:

• Francis J. Murray, John von Neumann, On Rings of Operators, Annals of Mathematics, Second Series, 37 1 (1936) 116-229 [doi:10.2307/1968693, jstor:1968693]

Discussion of traces on these factors:

• Francis J. Murray, John von Neumann, On rings of operators. II, Trans. Amer. Math. Soc. 41 (1937) 208-248 [doi:10.2307/1989620, jstor:1989620]

On isomorphism of factors and proof of a single isomorphism class of approximately finite type $II_1$ factors:

• Francis J. Murray, John von Neumann, On rings of operators. IV, Annals of Mathematics, Second Series, 44 4 (1943) 716-808 [doi:10.2307/1969107, jstor:1969107]

On decomposing von Neumann algebras as a direct integral of factors:

• John von Neumann, On rings of operators, reduction theory, Annals of Mathematics Second Series, Vol. 50, No. 2 (1949) [jstor:1969463]

Recollection of the history which made von Neumann turn to discussion of these “factors”, motivated from considerations in the foundations of quantum mechanics and quantum logic:

• Miklos Rédei, Why John von Neumann did not Like the Hilbert Space formalism of quantum mechanics (and what he liked instead), Studies in History and Philosophy of Modern Physics 27 4 (1996) 493-510 [doi:10.1016/S1355-2198(96)00017-2]

category: people