Who was a Hungarian-American mathematician, physicist, and computer scientist that helped introduce a technique for using unbounded operators to study modules generated by a single vector?
Affiliated operator In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that index theorems for elliptic operators on closed manifolds with infinite fundamental group could naturally be phrased in terms of unbounded operators affiliated with the von Neumann algebra of the group. Algebraic properties of affiliated operators have proved important in L cohomology, an area between analysis and geometry that evolved from the study of such index theorems.
Farkas Bolyai Farkas Bolyai (] ; 9 February 1775 – 20 November 1856; also known as Wolfgang Bolyai in Germany) was a Hungarian mathematician, mainly known for his work in geometry.