Von Neumann algebras | Operator theory

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 L2 cohomology, an area between analysis and geometry that evolved from the study of such index theorems. (Wikipedia).

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Related pages

Elliptic operator | *-algebra | Spectral theorem | Domain of a function | Unitary operator | Partial isometry | Closed manifold | John von Neumann | Tomita–Takesaki theory | Francis Joseph Murray | Mathematics | Unbounded operator | Von Neumann regular ring | Polar decomposition | Analysis | Self-adjoint | Von Neumann algebra | Isadore Singer | Convergence in measure | Fundamental group | Hilbert space | Geometry | Hilbert–Schmidt operator