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Untangling Noncommutativity with Operator Integrals

Emergence of Operator Integration Operator integration (OI) is a collection of powerful methods and techniques that enable analysis of functions with noncommuting arguments. Such functions arise, in particular, in various problems of applied matrix analysis, mathematical physics, noncommutative geometry, and statistical estimation. Single operator integrals are basic tools in the classical functional calculus. For instance, a self-adjoint operator A densely defined in a separable Hilbert space admits the operator integral decomposition