Regular operators on partial inner product spaces

J.-P. Antoine; F. Mathot

Annales de l'I.H.P. Physique théorique (1982)

  • Volume: 37, Issue: 1, page 29-50
  • ISSN: 0246-0211

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Antoine, J.-P., and Mathot, F.. "Regular operators on partial inner product spaces." Annales de l'I.H.P. Physique théorique 37.1 (1982): 29-50. <http://eudml.org/doc/76162>.

@article{Antoine1982,
author = {Antoine, J.-P., Mathot, F.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {operators on a partial inner product space; regular operators; *-algebra; Op*-algebra; rigged Hilbert space formulation of quantum mechanics; representation theory of Lie algebras},
language = {eng},
number = {1},
pages = {29-50},
publisher = {Gauthier-Villars},
title = {Regular operators on partial inner product spaces},
url = {http://eudml.org/doc/76162},
volume = {37},
year = {1982},
}

TY - JOUR
AU - Antoine, J.-P.
AU - Mathot, F.
TI - Regular operators on partial inner product spaces
JO - Annales de l'I.H.P. Physique théorique
PY - 1982
PB - Gauthier-Villars
VL - 37
IS - 1
SP - 29
EP - 50
LA - eng
KW - operators on a partial inner product space; regular operators; *-algebra; Op*-algebra; rigged Hilbert space formulation of quantum mechanics; representation theory of Lie algebras
UR - http://eudml.org/doc/76162
ER -

References

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  1. [1] J.-P. Antoine and A. Grossmann, J. Funct. Anal., t. 23, 1976, p. 369-378. Zbl0359.46020MR438071
  2. [2] J.-P. Antoine and A. Grossmann, J. Funct. Anal., t. 23, 1976, p. 379-391. Zbl0359.46021MR438072
  3. [3] J.-P. Antoine, J. Math. Phys., t. 21, 1980, p. 268-279. Zbl0477.46005MR558469
  4. [4] J.-P. Antoine, J. Math. Phys., t. 21, 1980, p. 2067-2079. Zbl0477.46006MR579203
  5. [5] R.T. Powers, Commun. Math. Phys., t. 21, 1971, p. 85-124. Zbl0214.14102MR283580
  6. [6] G. Lassner, Reports Math. Phys., t. 3, 1972, p. 279-293 ; Wiss. Z. Karl-Marx-Univ. Leipzig, Math. Naturwiss R., t. 24, 1975, p. 465-471. Zbl0252.46087MR322527
  7. [7] R. Ascoli, G. Epifanio, A. Restivo, Comm. Math. Phys., t. 18, 1970, p. 291-300 ; Riv. Math. Univ. Parma, t. 3, 1974, p. 21-32. Zbl0197.53502MR272300
  8. [8] A. Inoue, Pacific J. Math., t. 65, 1976, p. 77-95 ; ibid., t. 66, 1976, p. 411-431 ; ibid., t. 69, 1977, p. 105-115. Zbl0331.46063
  9. [9] S. Gudder and W. Scruggs, Pacific J. Math., t. 70, 1977, p. 369-382. Zbl0374.46045MR482269
  10. [10] G. Epifanio and C. Trapani, J. Math. Phys., t. 22, 1981, p. 974-978. Zbl0459.47033MR622846
  11. [11] J.-P. Antoine and F. Mathot, Partial inner product spaces generated by algebras of unbounded operators, Preprint UCL-IPT-81-10 (to appear). Zbl0629.46048
  12. [12] A. Böhm, The Rigged Hilbert Space in Quantum Mechanics. Springer Lecture Notes in Physics, t. 78, 1978, and earlier references therein. Zbl0388.46045MR503149
  13. [13] J.E. Roberts, J. Math. Phys., t. 7, 1966, p. 1097-1104 ; Commun. Math. Phys., t. 3, 1966, p. 98-119. Zbl0144.23404MR216836
  14. [14] J.-P. Antoine, J. Math. Phys., t. 10, 1969, p. 53-69 ; ibid., t. 10, 1969, p. 2276-2290. Zbl0172.56602
  15. [15] H.J. Borchers, Decomposition of families of unbounded operators, in RCP 25, Strasbourg, t. 22, 1975, p. 26-59. MR673613
  16. H.J. Borchers and J. Yngvason, Comm. Math. Phys., t. 42, 1975, p. 231-252. Zbl0307.46053MR377550
  17. [16] L. Schwartz, J. Anal. Math. (Jerusalem), t. 13, 1964, p. 115-256. Zbl0124.06504
  18. [17] V. Bargmann, Commun. Pure Appl. Math., t. 20, 1967, p. 1-101. Zbl0149.09601
  19. [18] M. Friedrich and G. Lassner, Wiss. Z. Karl-Marx-Univ. Leipzig, Math. Naturwiss R., t. 27, 1978, p. 245-251 ; Rigged Hilbert spaces and topologies on operator algebras, Reports Math. Phys. (to appear). Zbl0404.47021MR524027
  20. [19] M. Reed and B. Simon, Methods of Modern Mathematical Physics, I. Functional Analysis, Academic Press, New York and London, 1975. MR751959
  21. [20] H.H. Schaefer, Ann. Math., t. 107, 1962, p. 125-173. Zbl0112.34303
  22. [21] F. Mathot, J. Math. Phys., t. 22, 1981, p. 1386-1389. Zbl0473.46038MR626127
  23. [22] G. Lassner and W. Timmermann, Reports Math. Phys., t. 3, 1972, p. 295-305. Zbl0252.46088MR423090
  24. [23] K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups, PWN, Warzawa, 1968. Zbl0185.39001MR247377
  25. [24] Ju.M. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence R. I., 1968 (Chap. V). Zbl0157.16601MR222718
  26. [25] A.O. Barut and R. Raczka, Theory of Group Representations and Applications, PWNWarszawa1977. Zbl0471.22021MR495836
  27. [26] F. Debacker-Mathot, Commun. Math. Phys., t. 42, 1975, p. 183-193. Zbl0303.46061MR467344
  28. [27] E. Nelson and W.F. Stinespring, Amer. J. Math., t. 81, 1959, p. 547-560. Zbl0092.32103MR110024
  29. E. Nelson, Ann. of Math., t. 70, 1959, p. 572-615. Zbl0091.10704MR107176
  30. [28] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Memoirs Amer. Math. Soc., t. 16, 1966,, Providence RI. Zbl0123.30301
  31. [29] J.-P. Antoine and A. Grossmann, J. Math. Phys., t. 19, 1978, p. 329-335. Zbl0372.46025

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