Operator inequalities and construction of Krein spaces |
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Authors: | Takuya Hara |
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Institution: | (1) Division of Applied Mathematics Research Institute of Applied Electricity, Hokkaido University, 060 Sapporo, Japan |
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Abstract: | Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. |
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Keywords: | Primary 46 C 20 Secondary 47 A 63 |
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