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