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

J 2015

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

JANDA, Jiří a Jan PASEKA

Základní údaje

Originální název

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

Autoři

JANDA, Jiří (203 Česká republika, domácí) a Jan PASEKA (203 Česká republika, garant, domácí)

Vydání

International Journal of Theoretical Physics, NEW YORK, Springer, 2015, 0020-7748

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 1.041

Kód RIV

RIV/00216224:14310/15:00085222

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s10773-015-2547-9

UT WoS

000364224200016

Klíčová slova anglicky

Effect algebra; Generalized effect algebra; Hilbert space; Operator; Unbounded operator; Bilinear form; Singular bilinear form

Štítky

AKR, rivok

Změněno: 13. 12. 2015 08:43, prof. RNDr. Jan Paseka, CSc.

Anotace

V originále

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.

Návaznosti

EE2.3.20.0051, projekt VaV

Název: Algebraické metody v kvantové logice

Citovat

JANDA, Jiří a Jan PASEKA. A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms. 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.

@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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