@article{AIHPA_1989__50_2_161_0,
author = {Antoine, J.-P. and Karwowski, W.},
title = {Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras},
journal = {Annales de l'I.H.P. Physique th\'eorique},
pages = {161--185},
year = {1989},
publisher = {Gauthier-Villars},
volume = {50},
number = {2},
mrnumber = {1002818},
zbl = {0678.47041},
language = {en},
url = {https://www.numdam.org/item/AIHPA_1989__50_2_161_0/}
}
TY - JOUR
AU - Antoine, J.-P.
AU - Karwowski, W.
TI - Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras
JO - Annales de l'I.H.P. Physique théorique
PY - 1989
SP - 161
EP - 185
VL - 50
IS - 2
PB - Gauthier-Villars
UR - https://www.numdam.org/item/AIHPA_1989__50_2_161_0/
LA - en
ID - AIHPA_1989__50_2_161_0
ER -
%0 Journal Article
%A Antoine, J.-P.
%A Karwowski, W.
%T Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras
%J Annales de l'I.H.P. Physique théorique
%D 1989
%P 161-185
%V 50
%N 2
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPA_1989__50_2_161_0/
%G en
%F AIHPA_1989__50_2_161_0
Antoine, J.-P.; Karwowski, W. Commuting normal operators in partial $L^2 (\mathbb {R}^2)$-algebras. Annales de l'I.H.P. Physique théorique, Tome 50 (1989) no. 2, pp. 161-185. https://www.numdam.org/item/AIHPA_1989__50_2_161_0/
[1] , Commun. Math. Phys., t. 21, 1971, p. 85 ; Trans. Amer. Math. Soc., t. 187, 1974, p. 261. | Zbl | MR
[2] , Reports Math. Phys., t. 3, 1972, p. 279 ; Wiss. Z. Karl-Marx-Univ. Leipzig, Math.-Naturwiss. R., t. 24, 1975, p. 465 ; t. 30, 1981, p. 572. | Zbl | MR
[3] and , Publ. RIMS, Kyoto Univ., t. 21, 1985, p. 205; Add. ibid., t. 22, 1986, p. 507. | Zbl | MR
[4] and , Ann. Inst. H. Poincaré, t. 46, 1987, p. 299. | Zbl | MR | Numdam
[5] and , Representations of partial *-algebras and sesquilinear forms (unpublished).
[6] , In: Spontaneous Symmetry Breakdown and Related Topics (Karpacz, 1985), p. 247-267 ; L. Michel, J. Mozrzymas and A. Pekalski (eds.) ; World Scientific, Singapore, 1985. | MR
[7] , and , Ann. Inst. H. Poincaré, t. 46, 1987, p. 325. | Zbl | MR | Numdam
[8] and , J. Math. Phys., t. 25, 1984, p. 2633. | Zbl | MR
[9] , Ann. Math., t. 70, 1959, p. 572. | Zbl | MR
[10] and , Methods of Modern Mathematical Physics. I. Functional Analysis. II. Fourier Analysis, Self-adjointness, Academic, New York, 1972, 1975 . | Zbl | MR
[11] , Acta Sci. Math. (Szeged), t. 47, 1984, p. 131 ; Manuscr. Math., t. 57, 1985, p. 221 ; Math. Nachr., t. 125, 1986, p. 83. and , J. Int. Eq. and Oper. Th., t. 7, 1984, p. 815. | Zbl
[12] and , Operator Commutation Relations, Reidel, Dordrecht and Boston, 1984. , J. Math. Anal. Appl., t. 123, 1987, p. 508. | Zbl | MR
[13] , and , Helv. Phys. Acta, t. 56, 1983, p. 1175. | MR
[14] , and , Partial *-algebras of closable operators. I. The general theory and the abelian case, preprint UCL-IPT-88-25 (to be published).
[15] , J. Math. Phys., t. 7, 1966, p. 1097 ; Commun. Math. Phys., t. 3, 1966, p. 98. | Zbl | MR
[16] . Boulder Lectures in Theoretical Physics, t. 9A, 1966, p. 255 ; The Rigged Hilbert Space and Quantum Mechanics, Lecture Notes in Physics, t. 78, Springer, Berlin, 1978. | Zbl
[17] , J. Math. Phys., t. 10, 1969, p. 53 et 2276. | Zbl
[18] and , Leçons d'Analyse Fonctionnelle, Gauthier-Villars, Paris and Akadémiai Kiado, Budapest, 1968.
[19] and , Theory of Linear Operators in Hilbert Spaces, I, II. F. Ungar, New York, 1966. | Zbl
[20] , Linear Operators in Hilbert Spaces, Springer, Berlin, 1980. | Zbl | MR
[21] and , Les Distributions, t. 4, Dunod, Paris, 1967. | Zbl
[22] and , Helv. Phys. Acta, t. 38, 1965, p. 30. | Zbl | MR
[23] , Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), Gauthier-Villars, Paris, 1957. | Zbl | MR
[24] , Direct Integral Theory, Marcel Dekker, New York, 1980. | Zbl | MR
[25] , and , Partial *-algebras of closable operators. II-IV (in preparation).
[26] , Commutation Properties of Hilbert Space Operators and Related Topics, Springer, Berlin, 1967. | Zbl
[27] , J. Math. Phys., t. 26, 1985, p. 1118. | Zbl | MR
[28] , Self-Adjoint Operators, Lect. Notes Math., t. 433, Springer, Berlin, 1975. | Zbl | MR
[29] , Measure Theory, Van Nostrand, Princeton, 1950. | Zbl | MR
[30] , Naive Set Theory, Van Nostrand, Princeton, 1961. | Zbl | MR






