@article{ASCFM_1991__97_27_1_0,
author = {Rodriguez Palacios, Angel},
title = {An approach to {Jordan-Banach} algebras from the theory of nonassociative complete normed algebras},
journal = {Annales scientifiques de l'Universit\'e de Clermont. Math\'ematiques},
pages = {1--57},
publisher = {UER de Sciences exactes et naturelles de l'Universit\'e de Clermont},
volume = {97},
number = {27},
year = {1991},
mrnumber = {1164710},
zbl = {0768.17014},
language = {en},
url = {https://www.numdam.org/item/ASCFM_1991__97_27_1_0/}
}
TY - JOUR AU - Rodriguez Palacios, Angel TI - An approach to Jordan-Banach algebras from the theory of nonassociative complete normed algebras JO - Annales scientifiques de l'Université de Clermont. Mathématiques PY - 1991 SP - 1 EP - 57 VL - 97 IS - 27 PB - UER de Sciences exactes et naturelles de l'Université de Clermont UR - https://www.numdam.org/item/ASCFM_1991__97_27_1_0/ LA - en ID - ASCFM_1991__97_27_1_0 ER -
%0 Journal Article %A Rodriguez Palacios, Angel %T An approach to Jordan-Banach algebras from the theory of nonassociative complete normed algebras %J Annales scientifiques de l'Université de Clermont. Mathématiques %D 1991 %P 1-57 %V 97 %N 27 %I UER de Sciences exactes et naturelles de l'Université de Clermont %U https://www.numdam.org/item/ASCFM_1991__97_27_1_0/ %G en %F ASCFM_1991__97_27_1_0
Rodriguez Palacios, Angel. An approach to Jordan-Banach algebras from the theory of nonassociative complete normed algebras. Annales scientifiques de l'Université de Clermont. Mathématiques, Tome 97 (1991) no. 27, pp. 1-57. https://www.numdam.org/item/ASCFM_1991__97_27_1_0/
1 , The radical of a non-associative algebra, Bull. Amer. Math. Soc. 48 (1942), 891-897. | Zbl | MR
2 , Absolute valued real algebras, Ann. of Math. 48 (1947), 495-501. | Zbl | MR
3 , Absolute valued algebraic algebras, Bull. Amer. Math. Soc. 55 (1949), 763-768. | Zbl | MR
4 , Compact convex sets and boundary Integrals, Erg. der Math. 57, Springer-Verlag, Berlin 1971. | Zbl | MR
5 , and , State spaces of C*-algebras, Acta Math. 144 (1980), 267-305. | Zbl | MR
6 , and , A Gelfand Neumark theorem for Jordan algebras, Adv. Math. 28 (1978), 11-56. | Zbl | MR
7 and , Real and complex noncommutative Jordan Banach algebras, Math. Z. 185 (1984), 105-113. | Zbl | MR
8 , , and , A non-smooth extension of Frechet differentiability of the norm with applications to numerical ranges, Glasgow Math. J. 28 (1986), 121-137. | Zbl | MR
9 and , Sobre el espectro de derivationes y automorfismos de las algebras de Banach, Rev. Real Acad. Cienc. Exactas, Fisicas y Naturales de Madrid 79 (1985), 113-118. | MR
10, The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 7-25. | Zbl | MR
11 J.M. BACHAR, W.G. BADE, P.C. CURTUS, H.G. DALES and M.P. THOMAS (Editors), Radical Banach Algebras and Automatic Continuity, Lect. Notes in Math. 975, Springer-Verlag, Berlin 1983. | Zbl | MR
12, Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229-247. | Zbl | MR
13 and , The continuity of derivations of Banach algebras, J. Funct. Anal. 16 (1974), 372-387. | Zbl | MR
14 and , Uniqueness of the norm topology in certain Banach Jordan algebras, Publ. Ramanujan Inst. 1 (1968/69), 283-289. | Zbl | MR
15 and , On biduals, preduals, and ideals of JB*-triples, University of California Irvine. Math. Scand. 59 (1986), 177-191. | Zbl | MR
16 and , Numerical ranges of operators on normed spaces and of elements of normed algebras, Lecture Notes Series 2, London Math. Soc., Cambridge 1971. | Zbl | MR
17 and , Numerical ranges II, Lecture Notes Series 10, London Math. Soc. Cambridge 1973. | Zbl | MR
18 and , Complete Normed Algebras, Erg. der Math. 80, Springer-Verlag, Berlin 1973. | Zbl | MR
19, Structure and representations of noncommutative C*-Jordan algebras, Manuscripta Math. 41 (1983), 139-171. | Zbl | MR
20, A Gelfand-Neumark theorem for C*-alternative algebras, Math. Z. 185 (1984), 225-242. | Zbl | MR
21, The theory and structure of dual JB-algebras, Math. Z. 180 (1982), 525-534. | Zbl | MR
22 and , Lie and Jordan structures in Banach algebras, Pacific J. Math. 15 (1965), 775-797. | Zbl | MR
23 , Sur la théorie des structures des H*-algebres de Jordan non commutatives. Colloque sur les algèbres de Jordan. Montpellier 1985.
24 and , Isomorphism of H*-algebras, Math. Proc. Camb. Phil. Soc. 97 (1985), 93-99. | Zbl | MR
25 and , Structure theory for noncommutative Jordan H*-algebras, J. Algebra, 106 (1987), 1-14. | Zbl | MR
26, 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. | Zbl | MR
27 , Les algèbres d'opérateurs dans l'espace Hilbertien, Deuxième édition. Gauthier-Villars, Paris 1969. | Zbl
28 , Noncommutative Jordan algebras with minimal inner ideals. Colloque sur les algèbres de Jordan, Montpellier 1985.
29 and , Primitive noncommutative Jordan algebras with nonzero socle, Proc. Amer. Math. Soc. 96 (1986), 199-206. | Zbl | MR
30 and , A Wedderburn theorem for nonassociative complete normed algebras, J. London Math. Soc. 33 (1986), 328-338. | Zbl | MR
31 and , Structure theory in alternative Banach algebras, Universidad de Granada. Preprint 1984.
32 , and , Geometrical implications of upper semicontinuity of the duality mapping on a Banach space, Pacific J. Math. 70 (1978), 99-108. | Zbl | MR
33 and , Jordan Operators Algebras, Monographs and Studies in Mathematics 21, Pitman, 1984. | Zbl | MR
34 , Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space, Lect. Notes in Math. 285, Springer-Verlag, Berlin 1972. | Zbl | MR
35 , Topics in ring theory, Chicago, Univ. of Chicago Press 1965. | Zbl
36 , Cônes autopolaires et algèbres de Jordan, Lect. Notes in Math. 1049, Springer-Verlag, Berlin 1984. | Zbl | MR
37 and , Banach-power-associative algebras and Jordan algebras, Ann. Inst. H. Poincaré 43 (1985), 211-225. | Zbl | MR | Numdam
38 , Structure of rings, Amer. Math. Soc. Coll. Publ. 37, Providence, R.I., Amer. Math. Soc. 1968. | Zbl | MR
39, A commutative semisimple annihilator Banach algebra which is not dual, Bull. Amer. Math. Soc. 73 (1967), 407-409. | Zbl | MR
40 and , Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073. | Zbl | MR
41, A representation theory for commutative topological algebras, Mem. Amer. Math. Soc. 7 (1951). | Zbl | MR
42, and , On a nonassociative Vidav-Palmer theorem, Quart. J. Math. Oxford (2), 32 (1981), 435-442. | Zbl | MR
43, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), 39-64. | Zbl | MR
44 , Primitive alternative rings and semisimplicity, Ann. of Math. 77 (1955), 725-730. | Zbl | MR
45, and , A generalization of commutative and alternative rings, Canad. J. Math. 22 (1970), 348-362. | Zbl | MR
46, Espaces L-facteurs de leurs biduaux: bonne disposition, meilleure approximation et propriété de Radon-Nikodym. Quart.J. Math. Oxford Ser. 38 (1987), 229-243. | Zbl | MR
47, Complex methods and the estimations of operator norms and spectra from real numerical ranges, J. Funct. Anal. 10 (1972), 482-495. | Zbl | MR
48 , Holomorphic functional calculus in Jordan-Banach algebras, Colloque sur les algèbres de Jordan. Montpellier 1985.
49, JV-algebras, Math. Proc. Camb. Phil. Soc. 87 (1980), 47-50. | Zbl | MR
50, , and , An approach to numerical ranges without Banach algebra theory, Illinois, J. Math. 29 (1985), 609-635. | Zbl | MR
51, A general theory of Jordan rings, Proc. Nat. Acad. Sci. USA 56 (1966), 1072-1079. | Zbl | MR
52, The radical of a Jordan algebra, Proc. Nat. Acad. Sci. USA 62 (1969), 671-678. | Zbl | MR
53, On Hertein's theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382-392. | Zbl | MR
54, Noncommutative Jordan rings, Trans. Amer. Math. Soc. 158 (1971), 1-33. | Zbl | MR
55, and , Semisummands and semiideals in Banach spaces, Israel J. Math. 51 (1985), 33-67. | Zbl | MR
56, Gateaux differentials in Banach algebras, Math. Z. 139 (1974), 23-34. | Zbl | MR
57 and, Jordan rings with nonzero socle, Trans. Amer. Math. Soc. 251 (1979), 375-387. | Zbl | MR
58, and , Noncommutative Jordan C*-algebras, Muniscripta Math. 37 (1982), 87-120. | Zbl | MR
59, and , Type I factor representations of noncommutative JB*- algebras, Proc. London Math. Soc. (3) 48 (1984), 428-444. | Zbl | MR
60 , Structure theorems for alternative H*-algebras, Math. Proc. Camb. Phil. Soc. 94 (1983), 437-446. | Zbl | MR
61 and , Banach-Jordan *-algebras, Proc. London. Math. Soc. (3) 41.(1980), 21-44. | Zbl | MR
62, A Vidav-Palmer theorem for Jordan C*-algebras and related topics, J. London Math. Soc. (2) 22 (1980), 318-332. | Zbl | MR
63, Non-associative normed algebras spanned by hermitian elements, Proc. London Math. Soc. (3) 47 (1983), 258-274. | Zbl | MR
64, The Uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15. | Zbl | MR
65, C*- algebras and W*-algebras, Erg. der Math. 60, Springer-Verlag, Berlin 1971. | Zbl | MR
66, Generalized standard algebras, J. Algebra 12 (1969) 376-417. | Zbl | MR
67, Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc. 95 (1960), 69-80. | Zbl | MR
68 , Cartan deocmposition for L*-algebras, Trans. Amer; Math. Soc. 98 (1961), 334-349. | Zbl | MR
69, Jordan homomorphism and derivations on a semisimple Banach algebra, Proc. Amer. Math. Soc. 24 (1970), 209-214. | Zbl | MR
70 , Automatic continuity of linear operators, London Math. Soc. Letc. Notes Series 21, Cambridge U. Press 1976. | Zbl | MR
71, The radical of an alternative ring, Ann. of Math. 49 (1948), 702-709. | Zbl | MR
72, The numerical range in the second dual of a Banach algebra, Math. Proc. Camb. Phil. Soc. 89 (1981), 301-307. | Zbl | MR
73, Power-associative regular real normed algebras, J. Austral. Math. Soc. 6 (1966), 193-209. | Zbl | MR
74, Symmetric Banach Manifolds and Jordan C*-algebras, North-Holland Mathematics Studies 104, Elsevier Science Publishers B.V., Amsterdam 1985. | Zbl | MR
75 and, Absolute-valued algebras, Proc. Amer. Math. Soc. 11 (1960), 861-866. | Zbl | MR
76, On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital. 4 (1968), 427-429. | MR
77, Hilbert space methods in the theory of Jordan algebras, Math. Proc. Camb. Phil. Soc. 78 (1974), 293-300. | Zbl
78 and , Hilbert space methods in the theory of Jordan algebras II, Math. Proc. Camb. Phil. Soc. 79 (1976), 307-319. | Zbl | MR
79, Absolute valued algebras, Proc. Nat. Acad. Sci. USA 39 (1953), 330-332. | Zbl | MR
80 , Jordan C*-algebras, Michigan Math. J. 24 (1977), 291-302. | Zbl | MR
81 and , On isometries of Jordan algebras, J. London Math. Soc. (2) 17 (1978), 339-344. | Zbl | MR
82, Closed prime ideals in topological rings, Proc. London Math. Soc. 24 (1972), 307-323. | Zbl | MR
83, Homomorphisms on normed algebras, Pacific J. Math. 8 (1958), 373-381. | Zbl | MR
84, A Vidav theorem for Banach Jordan algebras, Math. Proc. Camb. Phil. Soc. 84 (1978), 263-272. | Zbl | MR
85, Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. (2) 22 (1979), 93-104. | Zbl | MR
86, Non-unital Banach Jordan algebras and C*-triple systems, Proc. Edinburgh Math. Soc. (2) 24 (1981), 19-30. | Zbl
87, Coincidence of Smiley and Kleinfeld radicals in alternative rings, Algebra i Logika 8 (1969), 309-319. | Zbl | MR
88, and , A characterization of operator algebras, J. Funct. Anal. 89 (1990), 188-201. | Zbl | MR
89, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. | Zbl | MR
90, and , Structurable H*-algebras, J. Algebra (to appear). | Zbl
91 and , Extended centroid and central closure of semiprime normed algebras: a first approach, Commun. Algebra 18 (1990), 2293-2326. | Zbl | MR
92 and , Nonassociative ultraprime normed algebras, Quart. J. Math. Oxford (to appear). | Zbl
93 , Jordan derivations on rings, Proc. Amer; Math. Soc. 53 (1975), 321-324. | Zbl | MR
94, 3rd and , Prime nonassociative algebras, Pacific J. Math. 60 (1975), 49-63. | Zbl | MR
95, and , A Zelmanov prime theorem for JB*-algebras, J. London Math. Soc. (to appear).
96 and , Maximal modula inner ideals and the Jacobson radical of a Jordan algebra, J. Algebra 68 (1981), 156-169. | Zbl | MR
97, Rings of quotients of ultraprime Banach algebras, with applications to elementary operators, Proc. Centre Math. Anal. Austral. Nat. Univ. 21 (1989), 297-317. | Zbl | MR
98 , Primitive nonassociative normed algebras and extended centroid. In "Workshop on nonassociative algebraic models", Nova Science Publishers, New York (to appear). | Zbl | MR
99 , Continuity of derivations on H*-algebras. Preprint 1991. | Zbl | MR
100 , , and , Rings that are nearly associative, Acadepic Press 1982. | Zbl | MR
