Considerable Sets of Linear Operators in Hilbert Spaces as
Operator Generalized Effect Algebras

J 2011

Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras

PASEKA, Jan a Zdenka RIEČANOVÁ

Základní údaje

Originální název

Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí) a Zdenka RIEČANOVÁ (703 Slovensko)

Vydání

Foundations of Physics, NEW YORK, Springer Science+Business Media B. V. 2011, 0015-9018

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

Odkazy

URL

Impakt faktor

Impact factor: 1.055

Kód RIV

RIV/00216224:14310/11:00055104

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.1007/s10701-011-9573-0

UT WoS

000294505200004

Klíčová slova anglicky

Quantum structures; (Generalized) effect algebra; Hilbert space; (Unbounded) positive linear operator; Closure; Adjoint; Friedrichs extension

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 10. 4. 2012 08:19, prof. RNDr. Jan Paseka, CSc.

Anotace

V originále

We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.

Návaznosti

MSM0021622409, záměr

Název: Matematické struktury a jejich fyzikální aplikace

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Matematické struktury a jejich fyzikální aplikace

Citovat

PASEKA, Jan a Zdenka RIEČANOVÁ. Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras. Foundations of Physics. NEW YORK: Springer Science+Business Media B. V., 2011, roč. 41, č. 10, s. 1634-1647. ISSN 0015-9018. Dostupné z: https://dx.doi.org/10.1007/s10701-011-9573-0.

@article{967846,
   author = {Paseka, Jan and Riečanová, Zdenka},
   article_location = {NEW YORK},
   article_number = {10},
   doi = {http://dx.doi.org/10.1007/s10701-011-9573-0},
   keywords = {Quantum structures; (Generalized) effect algebra; Hilbert space; (Unbounded) positive linear operator; Closure; Adjoint; Friedrichs extension},
   language = {eng},
   issn = {0015-9018},
   journal = {Foundations of Physics},
   title = {Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras},
   url = {http://www.springerlink.com/content/34h7p0018736878x/},
   volume = {41},
   year = {2011}
}

TY  - JOUR
ID  - 967846
AU  - Paseka, Jan - Riečanová, Zdenka
PY  - 2011
TI  - Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras
JF  - Foundations of Physics
VL  - 41
IS  - 10
SP  - 1634-1647
EP  - 1634-1647
PB  - Springer Science+Business Media B. V.
SN  - 00159018
KW  - Quantum structures
KW  - (Generalized) effect algebra
KW  - Hilbert space
KW  - (Unbounded) positive linear operator
KW  - Closure
KW  - Adjoint
KW  - Friedrichs extension
UR  - http://www.springerlink.com/content/34h7p0018736878x/
L2  - http://www.springerlink.com/content/34h7p0018736878x/
N2  - We show that considerable sets of positive linear operators namely their extensions as closures, adjoints or Friedrichs positive self-adjoint extensions form operator (generalized) effect algebras. Moreover, in these cases the partial effect algebraic operation of two operators coincides with usual sum of operators in complex Hilbert spaces whenever it is defined. These sets include also unbounded operators which play important role of observables (e.g., momentum and position) in the mathematical formulation of quantum mechanics.
ER  -

PASEKA, Jan a Zdenka RIEČANOVÁ. Considerable Sets of Linear Operators in Hilbert Spaces as Operator Generalized Effect Algebras. \textit{Foundations of Physics}. NEW YORK: Springer Science+Business Media B. V., 2011, roč.~41, č.~10, s.~1634-1647. ISSN~0015-9018. Dostupné z: https://dx.doi.org/10.1007/s10701-011-9573-0.

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