JournalsprimsVol. 38 , No. 4DOI 10.2977/prims/1145476198

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

  • Gerald Hofmann

    HTWK Leipzig, Germany
On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces cover

Abstract

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.