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.
Michael Makkai Michael Makkai (Hungarian: "Makkai Mihály" , 24 June 1939 in Budapest, Hungary) is Canadian mathematician of Hungarian origin, specializing in mathematical logic. He works in model theory, category theory, algebraic logic, and in the theory of topoi. He was awarded his PhD from the Eötvös Loránd University, Budapest, in 1966, having been supervised by Rózsa Péter and Andrzej Mostowski. He then worked at the Mathematical Institute of the Hungarian Academy of Sciences. Between 1974 and 2010, he was professor of mathematics at the McGill University, retiring in 2010. He is an external member of the Hungarian Academy of Sciences (1995).