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@article{1320844,
author = {Janda, Jiří and Paseka, Jan},
article_location = {NEW YORK},
article_number = {12},
doi = {http://dx.doi.org/10.1007/s10773-015-2547-9},
keywords = {Effect algebra; Generalized effect algebra; Hilbert space; Operator; Unbounded operator; Bilinear form; Singular bilinear form},
language = {eng},
issn = {0020-7748},
journal = {International Journal of Theoretical Physics},
title = {A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms},
volume = {54},
year = {2015}
}
TY - JOUR
ID - 1320844
AU - Janda, Jiří - Paseka, Jan
PY - 2015
TI - A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms
JF - International Journal of Theoretical Physics
VL - 54
IS - 12
SP - 4349-4355
EP - 4349-4355
PB - Springer
SN - 00207748
KW - Effect algebra
KW - Generalized effect algebra
KW - Hilbert space
KW - Operator
KW - Unbounded operator
KW - Bilinear form
KW - Singular bilinear form
N2 - 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 that there 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.
ER -
JANDA, Jiří a Jan PASEKA. A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms. \textit{International Journal of Theoretical Physics}. NEW YORK: Springer, 2015, roč.~54, č.~12, s.~4349-4355. ISSN~0020-7748. Dostupné z: https://dx.doi.org/10.1007/s10773-015-2547-9.
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