Extension of the Hilbert Space by J-Unitary Transformations
نویسنده
چکیده
A theory of non-unitary unbounded similarity transformation operators is developed. To this end the class of J-unitary operators U is introduced. These operators are similar to unitary operators in their algebraic aspects but differ in their topological properties. It is shown how J-unitary operators are related to so-called J-biorthonormal systems and J-selfadjoint projections. Families {Uα} of J-unitary operators define in a natural way a Fréchet subspace of the Hilbert space H, the dual space of which constitutes an extension of H. The J-selfadjoint Hamilton operator H can also be regarded as a restriction of an operator H ′ defined on the extension of the Hilbert space. The advantages of a J-unitary transformation theory and the relation to other approaches in scattering theory are discussed.
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