Remarks on the bidual of Banach algebras (the C * case)

Bruno Iochum; Guy Loupias

Annales scientifiques de l'Université de Clermont. Mathématiques (1991)

  • Volume: 97, Issue: 27, page 107-118
  • ISSN: 0249-7042

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Iochum, Bruno, and Loupias, Guy. "Remarks on the bidual of Banach algebras (the $C^\ast $ case)." Annales scientifiques de l'Université de Clermont. Mathématiques 97.27 (1991): 107-118. <http://eudml.org/doc/80577>.

@article{Iochum1991,
author = {Iochum, Bruno, Loupias, Guy},
journal = {Annales scientifiques de l'Université de Clermont. Mathématiques},
keywords = {square; Arens regularity; Banach spaces with a binary product; Banach power-associative systems},
language = {eng},
number = {27},
pages = {107-118},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {Remarks on the bidual of Banach algebras (the $C^\ast $ case)},
url = {http://eudml.org/doc/80577},
volume = {97},
year = {1991},
}

TY - JOUR
AU - Iochum, Bruno
AU - Loupias, Guy
TI - Remarks on the bidual of Banach algebras (the $C^\ast $ case)
JO - Annales scientifiques de l'Université de Clermont. Mathématiques
PY - 1991
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 97
IS - 27
SP - 107
EP - 118
LA - eng
KW - square; Arens regularity; Banach spaces with a binary product; Banach power-associative systems
UR - http://eudml.org/doc/80577
ER -

References

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  2. 2 R. Arens, Operations induced in function classes, Monatshefte für Math.55 (1951), 839-848. Zbl0044.32601MR44109
  3. 3 F.F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, Cambridge University Press, (1971). Zbl0207.44802MR288583
  4. 4 N. Bourbaki, Topologie générale, Herman (1971). MR358652
  5. 5 P. Civin and B. Yood, The second conjugate space of a Banach algebra as an algebra, Pac. J. Math11 (1961), 847-870. Zbl0119.10903MR143056
  6. 6 S. Dineen, The second dual of a JB * - triple system, Complex analysis, functional analysis and approximation theory (Campinas, 1984) 67-69, North-Holland Math. Stud., 125, North-Holland, Amsterdam - New York, 1986. Zbl0653.46053MR893410
  7. 7 J. Duncan and S.A.R. Hosseinium, The second dual of a Banach algebraProc. Royal Soc. Edinburgh, A84 (1979), 309-325. Zbl0427.46028MR559675
  8. 8 G. Godefroy, Parties admissibles d'un espace de Banach. Applications, Ann. Scient. Ecole Norm. Sup.16 (1983), 109-122. Zbl0544.46011MR719765
  9. 9 H. Hanche-Olsen and E. Stormer, Jordan operator algebras, Pitman (1984). Zbl0561.46031MR755003
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  11. 11 S. Heinrich and P. Mankiewicz, Applications of ultraproducts to the uniform and Lipschitz classification of Banach spaces, Studia Math.73 (1982), 225-251. Zbl0506.46008MR675426
  12. 12 B. Iochum and G. Loupias, Banach power-associative algebras and Jordan algebras, Ann. Institut H. Poincaré.43 (1985), 211-225. Zbl0587.17012MR817536
  13. 13 W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z.183 (1983), 503-529. Zbl0519.32024MR710768
  14. 14 R. Paya, J. Perez and A. Rodriguez, Non commutative Jordan C*algebras, Manuscripta Math.37 (1982), 87-120. Zbl0483.46049MR649567
  15. 15 A. Rodriguez-Palacios, A Vidav-Palmer theorem for Jordan C*algebras and relatied topics, J. London Math. Soc.22 (1980), 318-332. Zbl0483.46050MR588278
  16. 16 A. Rodriguez-Palacios, Non associative normed algebras spanned by hermitian elements, Proc. London Math. Soc.47 (1983), 258-279. Zbl0521.47036
  17. 17 S. Sakai, C*algebras and W*algebras, Erg. der Math.60, Springer-Verlag (1971). Zbl0219.46042MR442701
  18. 18 R.D. Schafer, An introduction to non associative algebras, Academic Press, New York (1966). Zbl0145.25601
  19. 19 M.A. Youngson, Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc.22 (1979), 169-180. Zbl0414.46034MR549462

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