▁▁ ▁Category : Sw iss ▁women ▁scient ists ▁Category : É cole ▁Poly te chni que ▁F éd éra le ▁de ▁La us anne ▁fac ulty ▁Category : Univers ity ▁of ▁Bern ▁al umn i ▁Category : ET H ▁Zur ich ▁fac ulty ▁Category : Univers ity ▁of ▁Pennsylvania ▁fell ows ▁Category : Year ▁of ▁birth ▁missing ▁( l iving ▁people ) ▁Category : L iving ▁people <0x0A> </s> ▁In ▁mathematics , ▁a ▁von ▁Ne umann ▁algebra ▁or ▁W * - algebra ▁is ▁a ▁* - algebra ▁of ▁bounded ▁operators ▁on ▁a ▁Hil bert ▁space ▁that ▁is ▁closed ▁in ▁the ▁weak ▁operator ▁topology ▁and ▁contains ▁the ▁identity ▁operator . ▁It ▁is ▁a ▁special ▁type ▁of ▁C * - algebra . ▁ ▁Von ▁Ne umann ▁al gebras ▁were ▁originally ▁introduced ▁by ▁John ▁von ▁Ne umann , ▁motiv ated ▁by ▁his ▁study ▁of ▁single ▁operators , ▁group ▁representations , ▁er god ic ▁theory ▁and ▁quantum ▁mechan ics . ▁His ▁double ▁commut ant ▁theorem ▁shows ▁that ▁the ▁analyt ic ▁definition ▁is ▁equivalent ▁to ▁a ▁purely ▁algebraic ▁definition ▁as ▁an ▁algebra ▁of ▁symmet ries . ▁ ▁Two ▁basic ▁examples ▁of ▁von ▁Ne umann ▁al gebras ▁are ▁as ▁follows : ▁The ▁ring ▁ ▁of ▁essentially ▁bounded ▁meas urable ▁functions ▁on ▁the ▁real ▁line ▁is ▁a ▁commut ative ▁von ▁Ne umann ▁algebra , ▁whose ▁elements ▁act ▁as ▁multiplication ▁operators ▁by ▁point wise ▁multiplication ▁on ▁the ▁Hil bert ▁space ▁ ▁of ▁square - inte gra ble ▁functions . ▁The ▁algebra ▁ ▁of ▁all ▁bounded ▁operators ▁on ▁a ▁Hil bert ▁space