Mathematical Sciences: Domains of Derivations

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9424370 Akemann Unbounded derivations of operator algebras have been studied extensively as a model for the infinitesimal time development of a quantum-mechanical system. The proposed research involves a study of unbounded derivations of von Neumann algebras building on Weaver's characterization of the domains of such derivations as Lipschitz algebras, in the commutative case. Operators on a Hilbert space are infinite analogues of finite matrices. They have applications throughout mathematics but the proposed research relates specifically to mathematical physics. Algebras of operators have been used to model certain quantum mechanical systems, particularly those arising in quantum statistical mechanics. The proposal involves a change of the type of operator algebra used in this manner, with the double aim of clarifying the general theory and giving insight into specific examples. ***