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Hilbert superspace
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A theory of Hilbert superspace over an infinite dimensional Grassmann algebra Λ is given. Axioms of Hilbert superspace are given and it is proven that a Hilbert superspace is isomorphic to H⊗Λ for some Hilbert space H. A natural topology on it called ε topology is defined and continuous Λ-linear operators, especially unitary operators are studied. A Hilbert subsuperspace is defined and it is proven that its orthogonal complement is a Hilbert subsuperspace.
Title: Hilbert superspace
Description:
A theory of Hilbert superspace over an infinite dimensional Grassmann algebra Λ is given.
Axioms of Hilbert superspace are given and it is proven that a Hilbert superspace is isomorphic to H⊗Λ for some Hilbert space H.
A natural topology on it called ε topology is defined and continuous Λ-linear operators, especially unitary operators are studied.
A Hilbert subsuperspace is defined and it is proven that its orthogonal complement is a Hilbert subsuperspace.
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