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.
Cite this article
Gerald Hofmann, On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces. Publ. Res. Inst. Math. Sci. 38 (2002), no. 4, pp. 895–922DOI 10.2977/PRIMS/1145476198