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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© 1992 American Institute of Physics.
1992
American Institute of Physics
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