Algebra von Neumann

Dalam matematik, algebra von Neumann atau algebra-W* ialah algebra-* pengendali yang terikat dengan ruang Hilbert yang tertutup dalam topologi operator yang lemah dan mengandungi identiti pengendali. Ini ialah jenis khas algebra-C*.

Algebra Von Neumann pada awalnya diperkenalkan oleh John von Neumann, didorong oleh kajiannya mengenai pengendali tunggal, perwakilan kumpulan, teori ergodik dan mekanik kuantum. Teorem penggantian berganda menunjukkan bahawa definisi analitik sama dengan definisi algebra yang murni.

Rujukan

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 (A translation of , the first book about von Neumann algebras.)
; incomplete notes from a course.
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 A historical account of the discovery of von Neumann algebras.
. This paper gives their basic properties and the division into types I, II, and III, and in particular finds factors not of type I.  
. This is a continuation of the previous paper, that studies properties of the trace of a factor. 
. This studies when factors are isomorphic, and in particular shows that all approximately finite factors of type II1 are isomorphic. 

. The original paper on von Neumann algebras.
. This defines the ultrastrong topology.
. This discusses infinite tensor products of Hilbert spaces and the algebras acting on them.
. This shows the existence of factors of type III. 
. This shows that some apparently topological properties in von Neumann algebras can be defined purely algebraically. 
. This discusses how to write a von Neumann algebra as a sum or integral of factors.
. Reprints von Neumann's papers on von Neumann algebras.

Teori pengendali

John von Neumann