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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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