ISSN:
1420-8989
Keywords:
Primary, 46 C 20
;
Secondary, 47 A 63
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let $$\mathcal{H}$$ be a Hilbert space. A continuous positive operatorT on $$\mathcal{H}$$ uniquely determines a Hilbert space $$\mathcal{G}$$ which is continuously imbedded in $$\mathcal{H}$$ and for which $$T = E_\mathcal{G} E_\mathcal{G} ^* $$ with the canonical imbedding $$E_\mathcal{G} $$ . 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 ( $$\mathcal{K},J_\mathcal{K} $$ ) which is continuously imbedded in $$\mathcal{H}$$ and for which $$T = E_\mathcal{K} J_\mathcal{K} E_\mathcal{K} ^* $$ with the canonical imbedding $$E_\mathcal{K} $$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01195779
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