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On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces
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For developing a theory of
^*
-representations of
^*
-algebras
\mathcal A
on (indefinite) inner product spaces
E,(\cdot, \cdot)
, 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,(\cdot, \cdot)
to be a pseudo-Krein and pre-Krein space, respectively, are given. The results are illustrated by some examples.
European Mathematical Society - EMS - Publishing House GmbH
Title: On Inner Characterizations of Pseudo-Krein and Pre-Krein Spaces
Description:
For developing a theory of
^*
-representations of
^*
-algebras
\mathcal A
on (indefinite) inner product spaces
E,(\cdot, \cdot)
, 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,(\cdot, \cdot)
to be a pseudo-Krein and pre-Krein space, respectively, are given.
The results are illustrated by some examples.
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