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 and Jan PASEKA

Basic information

Original name

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

Authors

JANDA, Jiří (203 Czech Republic, belonging to the institution) and Jan PASEKA (203 Czech Republic, guarantor, belonging to the institution)

Edition

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

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Impact factor

Impact factor: 1.041

RIV identification code

RIV/00216224:14310/15:00085222

Organization unit

Faculty of Science

DOI

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

UT WoS

000364224200016

Keywords in English

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

Abstract

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.

Links

EE2.3.20.0051, research and development project

Name: Algebraické metody v kvantové logice

Citovat

JANDA, Jiří and Jan PASEKA. A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms. International Journal of Theoretical Physics. NEW YORK: Springer, 2015, vol. 54, No 12, p. 4349-4355. ISSN 0020-7748. Available from: 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 and Jan PASEKA. A Hilbert Space Operator Representation of Abelian Po-Groups of Bilinear Forms. \textit{International Journal of Theoretical Physics}. NEW YORK: Springer, 2015, vol.~54, No~12, p.~4349-4355. ISSN~0020-7748. Available from: https://dx.doi.org/10.1007/s10773-015-2547-9.

Detailed Information on Publication Record