▁functions . ▁ ▁See ▁also ▁ ▁A W * - algebra ▁ ▁References ▁ ▁, ▁▁▁ ▁. ▁ ▁( A ▁translation ▁of ▁, ▁the ▁first ▁book ▁about ▁von ▁Ne umann ▁al gebras .) ▁; ▁incomplete ▁notes ▁from ▁a ▁course . ▁. ▁▁ ▁A ▁historical ▁account ▁of ▁the ▁discovery ▁of ▁von ▁Ne umann ▁al gebras . ▁. ▁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 ▁continu ation ▁of ▁the ▁previous ▁paper , ▁that ▁studies ▁properties ▁of ▁the ▁trace ▁of ▁a ▁factor . ▁ ▁. ▁This ▁studies ▁when ▁factors ▁are ▁is omorphic , ▁and ▁in ▁particular ▁shows ▁that ▁all ▁approximately ▁finite ▁factors ▁of ▁type ▁II 1 ▁are ▁is omorphic . ▁▁ ▁. ▁The ▁original ▁paper ▁on ▁von ▁Ne umann ▁al gebras . ▁. ▁This ▁defines ▁the ▁ul tr astr ong ▁topology . ▁. ▁This ▁discuss es ▁infinite ▁tensor ▁products ▁of ▁Hil bert ▁spaces ▁and ▁the ▁al gebras ▁acting ▁on ▁them . ▁. ▁This ▁shows ▁the ▁existence ▁of ▁factors ▁of ▁type ▁III . ▁ ▁. ▁This ▁shows ▁that ▁some ▁apparently ▁topological ▁properties ▁in ▁von ▁Ne umann ▁al gebras ▁can ▁be ▁defined ▁purely ▁algebra ically . ▁ ▁. ▁This ▁discuss es ▁how ▁to ▁write ▁a ▁von ▁Ne umann ▁algebra ▁as ▁a ▁sum ▁or ▁integral ▁of ▁factors . ▁. ▁Re print s ▁von ▁Ne umann ' s ▁papers ▁on ▁von ▁Ne umann ▁al gebras . ▁ ▁Category : Operator ▁theory ▁* ▁Category :