# Circular operators related to some quantum observables

Annales Polonici Mathematici (1997)

- Volume: 66, Issue: 1, page 253-261
- ISSN: 0066-2216

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topWacław Szymański. "Circular operators related to some quantum observables." Annales Polonici Mathematici 66.1 (1997): 253-261. <http://eudml.org/doc/269999>.

@article{WacławSzymański1997,

abstract = {Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.},

author = {Wacław Szymański},

journal = {Annales Polonici Mathematici},

keywords = {circular operator; canonical commutation relation; circular operators; operator of multiplication by a homomorphism of a locally compact Abelian group; quantum observables},

language = {eng},

number = {1},

pages = {253-261},

title = {Circular operators related to some quantum observables},

url = {http://eudml.org/doc/269999},

volume = {66},

year = {1997},

}

TY - JOUR

AU - Wacław Szymański

TI - Circular operators related to some quantum observables

JO - Annales Polonici Mathematici

PY - 1997

VL - 66

IS - 1

SP - 253

EP - 261

AB - Circular operators related to the operator of multiplication by a homomorphism of a locally compact abelian group and its restrictions are completely characterized. As particular cases descriptions of circular operators related to various quantum observables are given.

LA - eng

KW - circular operator; canonical commutation relation; circular operators; operator of multiplication by a homomorphism of a locally compact Abelian group; quantum observables

UR - http://eudml.org/doc/269999

ER -

## References

top- [AHHK] W. Arveson, D. Hadwin, T. B. Hoover and E. Kymala, Circular operators, Indiana Univ. Math. J. 33 (1984), 583-595.
- [D] J. Dixmier, Von Neumann Algebras, North-Holland, 1981.
- [Ha] P. R. Halmos, Measure Theory, Van Nostrand, 1964.
- [Ho] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, North-Holland, 1982. Zbl0497.46053
- [I] E. K. Infantis, Abstract formulation of the quantum mechanical oscillator phase problem, J. Math. Phys. 12 (1971), 1021-1026. Zbl0212.16103
- [M1] W. Mlak, Notes on quantum circular operators, Institute of Mathematics, Polish Academy of Sciences, preprint 303, 1984.
- [M2] W. Mlak, Notes on circular operators I, II, III, IV, Univ. Iagel. Acta Math. 29 (1992), 145-180.
- [MS] W. Mlak and M. Słociński, Quantum phase and circular operators, Univ. Iagel. Acta Math., 133-144. Zbl0768.47011

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