Hilbert superspace
Copyright policy )Hilbert superspace
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.
- Toho University Japan
- University of Tokushima Japan
Hilbert superspace, Inner product spaces and their generalizations, Hilbert spaces, unitary operators, orthogonal complement, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, supernumbers, infinite dimensional Grassmann algebra, Hilbert subsuperspace
Hilbert superspace, Inner product spaces and their generalizations, Hilbert spaces, unitary operators, orthogonal complement, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, supernumbers, infinite dimensional Grassmann algebra, Hilbert subsuperspace
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