A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F15%3A00085222" target="_blank" >RIV/00216224:14310/15:00085222 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10773-015-2547-9" target="_blank" >http://dx.doi.org/10.1007/s10773-015-2547-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-015-2547-9" target="_blank" >10.1007/s10773-015-2547-9</a>

Result language
angličtina
Original language name
A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms
Original language description
The existence of a non-trivial singular positive bilinear form Simon (J. Funct. Analysis 28, 377-385 (1978)) yields that on an infinite-dimensional complex Hilbert space the set of bilinear forms is richer than the set of linear operators . We show thatthere exists an structure preserving embedding of partially ordered groups from the abelian po-group of symmetric bilinear forms with a fixed domain D on a Hilbert space into the po-group of linear symmetric operators on a dense linear subspace of an infinite dimensional complex Hilbert spacel (2)(M). Moreover, if we restrict ourselves to the positive parts of the above mentioned po-groups, we can embed positive bilinear forms into corresponding positive linear operators.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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