Publications of the Research Institute for Mathematical Sciences

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Volume 38, Issue 4, 2002, pp. 895–922
DOI: 10.2977/prims/1145476198

Published online: 2002-12-31

On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces

Gerald Hofmann[1]

(1) HTWK Leipzig, Germany

For developing a theory of *-representations of *-algebras A on (indefinite) inner product spaces E,(∙, ∙), the classes of pseudo-Krein and pre-Krein spaces which admit a Hilbert space structure and exactly one maximal Hilbert space structure, respectively, are introduced. Inner characterizations for the topological structure of E,(∙, ∙) to be a pseudo-Krein and pre-Krein space, respectively, are given. The results are illustrated by some examples.

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Hofmann Gerald: On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces. Publ. Res. Inst. Math. Sci. 38 (2002), 895-922. doi: 10.2977/prims/1145476198