Remarks on the bidual of Banach algebras (the C * case)
Iochum, Bruno ; Loupias, Guy
Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991), p. 107-118 / Harvested from Numdam
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Publié le : 1991-01-01
@article{ASCFM_1991__97_27_107_0,
     author = {Iochum, Bruno and Loupias, Guy},
     title = {Remarks on the bidual of Banach algebras (the $C^\ast $ case)},
     journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
     volume = {97},
     year = {1991},
     pages = {107-118},
     mrnumber = {1164713},
     zbl = {0781.46049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASCFM_1991__97_27_107_0}
}

Iochum, Bruno; Loupias, Guy. Remarks on the bidual of Banach algebras (the $C^\ast $ case). Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) pp. 107-118. http://gdmltest.u-ga.fr/item/ASCFM_1991__97_27_107_0/

1 R. Arens, The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848. | MR 45941 | Zbl 0044.32601

2 R. Arens, Operations induced in function classes, Monatshefte für Math. 55 (1951), 839-848. | MR 44109 | Zbl 0044.32601

3 F.F. Bonsall and J. Duncan, Numerical ranges of operators on normed spaces and of elements of normed algebras, Cambridge University Press, (1971). | MR 288583 | Zbl 0207.44802

4 N. Bourbaki, Topologie générale, Herman (1971). | MR 358652

5 P. Civin and B. Yood, The second conjugate space of a Banach algebra as an algebra, Pac. J. Math 11 (1961), 847-870. | MR 143056 | Zbl 0119.10903

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. | MR 893410 | Zbl 0653.46053

7 J. Duncan and S.A.R. Hosseinium, The second dual of a Banach algebra Proc. Royal Soc. Edinburgh, A 84 (1979), 309-325. | MR 559675 | Zbl 0427.46028

8 G. Godefroy, Parties admissibles d'un espace de Banach. Applications, Ann. Scient. Ecole Norm. Sup. 16 (1983), 109-122. | Numdam | MR 719765 | Zbl 0544.46011

9 H. Hanche-Olsen and E. Stormer, Jordan operator algebras, Pitman (1984). | MR 755003 | Zbl 0561.46031

10 S. Heinrich, Ultraproducts in Banach space theory, J. Reine. Ang. Math. 313 (1980), 72-104. | MR 552464 | Zbl 0412.46017

11 S. Heinrich and P. Mankiewicz, Applications of ultraproducts to the uniform and Lipschitz classification of Banach spaces, Studia Math. 73 (1982), 225-251. | MR 675426 | Zbl 0506.46008

12 B. Iochum and G. Loupias, Banach power-associative algebras and Jordan algebras, Ann. Institut H. Poincaré. 43 (1985), 211-225. | Numdam | MR 817536 | Zbl 0587.17012

13 W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. Math. Z. 183 (1983), 503-529. | MR 710768 | Zbl 0519.32024

14 R. Paya, J. Perez and A. Rodriguez, Non commutative Jordan C*algebras, Manuscripta Math. 37 (1982), 87-120. | MR 649567 | Zbl 0483.46049

15 A. Rodriguez-Palacios, A Vidav-Palmer theorem for Jordan C*algebras and relatied topics, J. London Math. Soc. 22 (1980), 318-332. | MR 588278 | Zbl 0483.46050

16 A. Rodriguez-Palacios, Non associative normed algebras spanned by hermitian elements, Proc. London Math. Soc. 47 (1983), 258-279. | Zbl 0521.47036

17 S. Sakai, C*algebras and W*algebras, Erg. der Math. 60, Springer-Verlag (1971). | MR 442701 | Zbl 0219.46042

18 R.D. Schafer, An introduction to non associative algebras, Academic Press, New York (1966). | Zbl 0145.25601

19 M.A. Youngson, Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. 22 (1979), 169-180. | MR 549462 | Zbl 0414.46034