@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}, volume = {97}, year = {1991}, pages = {1-57}, mrnumber = {1164710}, zbl = {0768.17014}, language = {en}, url = {http://dml.mathdoc.fr/item/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) pp. 1-57. http://gdmltest.u-ga.fr/item/ASCFM_1991__97_27_1_0/
1 The radical of a non-associative algebra, Bull. Amer. Math. Soc. 48 (1942), 891-897. | MR 7396 | Zbl 0061.05001
,2 Absolute valued real algebras, Ann. of Math. 48 (1947), 495-501. | MR 20550 | Zbl 0029.01001
,3 Absolute valued algebraic algebras, Bull. Amer. Math. Soc. 55 (1949), 763-768. | MR 30941 | Zbl 0033.34901
,4 Compact convex sets and boundary Integrals, Erg. der Math. 57, Springer-Verlag, Berlin 1971. | MR 445271 | Zbl 0209.42601
,5 State spaces of C*-algebras, Acta Math. 144 (1980), 267-305. | MR 573454 | Zbl 0458.46047
, and ,6 A Gelfand Neumark theorem for Jordan algebras, Adv. Math. 28 (1978), 11-56. | MR 482210 | Zbl 0397.46065
, and ,7 Real and complex noncommutative Jordan Banach algebras, Math. Z. 185 (1984), 105-113. | MR 724047 | Zbl 0513.46044
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 848419 | Zbl 0604.46021
, , 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 835174
and ,10The uniqueness of the complete norm topology in Banach algebras and Banach Jordan algebras, J. Funct. Anal. 47 (1982), 7-25. | MR 663830 | Zbl 0488.46043
,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 697577 | Zbl 0492.00008
12Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229-247. | MR 244762 | Zbl 0164.15701
,13The continuity of derivations of Banach algebras, J. Funct. Anal. 16 (1974), 372-387. | MR 358354 | Zbl 0296.46049
and ,14Uniqueness of the norm topology in certain Banach Jordan algebras, Publ. Ramanujan Inst. 1 (1968/69), 283-289. | MR 270153 | Zbl 0205.42204
and ,15On biduals, preduals, and ideals of JB*-triples, University of California Irvine. Math. Scand. 59 (1986), 177-191. | MR 884654 | Zbl 0621.46044
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 288583 | Zbl 0207.44802
and ,17 Numerical ranges II, Lecture Notes Series 10, London Math. Soc. Cambridge 1973. | MR 442682 | Zbl 0262.47001
and ,18Complete Normed Algebras, Erg. der Math. 80, Springer-Verlag, Berlin 1973. | MR 423029 | Zbl 0271.46039
and ,19Structure and representations of noncommutative C*-Jordan algebras, Manuscripta Math. 41 (1983), 139-171. | MR 689135 | Zbl 0512.46055
,20A Gelfand-Neumark theorem for C*-alternative algebras, Math. Z. 185 (1984), 225-242. | MR 731343 | Zbl 0514.46047
,21The theory and structure of dual JB-algebras, Math. Z. 180 (1982), 525-534. | MR 667006 | Zbl 0518.46053
,22Lie and Jordan structures in Banach algebras, Pacific J. Math. 15 (1965), 775-797. | MR 188813 | Zbl 0135.35701
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 764497 | Zbl 0571.46036
and ,25Structure theory for noncommutative Jordan H*-algebras, J. Algebra, 106 (1987), 1-14. | MR 878465 | Zbl 0616.46047
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 893410 | Zbl 0653.46053
,27 Les algèbres d'opérateurs dans l'espace Hilbertien, Deuxième édition. Gauthier-Villars, Paris 1969. | Zbl 0088.32304
,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 818443 | Zbl 0585.17001
and ,30A Wedderburn theorem for nonassociative complete normed algebras, J. London Math. Soc. 33 (1986), 328-338. | MR 838645 | Zbl 0603.46056
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 526669 | Zbl 0399.46012
, and ,33Jordan Operators Algebras, Monographs and Studies in Mathematics 21, Pitman, 1984. | MR 755003 | Zbl 0561.46031
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 476820 | Zbl 0256.22015
,35 Topics in ring theory, Chicago, Univ. of Chicago Press 1965. | Zbl 0232.16001
,36 Cônes autopolaires et algèbres de Jordan, Lect. Notes in Math. 1049, Springer-Verlag, Berlin 1984. | MR 764767 | Zbl 0556.46040
,37Banach-power-associative algebras and Jordan algebras, Ann. Inst. H. Poincaré 43 (1985), 211-225. | Numdam | MR 817536 | Zbl 0587.17012
and ,38 Structure of rings, Amer. Math. Soc. Coll. Publ. 37, Providence, R.I., Amer. Math. Soc. 1968. | MR 222106 | Zbl 0073.02002
,39A commutative semisimple annihilator Banach algebra which is not dual, Bull. Amer. Math. Soc. 73 (1967), 407-409. | MR 206739 | Zbl 0154.38703
,40Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1073. | MR 239419 | Zbl 0179.18103
and ,41A representation theory for commutative topological algebras, Mem. Amer. Math. Soc. 7 (1951). | MR 44040 | Zbl 0042.34801
,42On a nonassociative Vidav-Palmer theorem, Quart. J. Math. Oxford (2), 32 (1981), 435-442. | MR 635592 | Zbl 0446.46043
, and ,43Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), 39-64. | MR 454091 | Zbl 0335.58005
,44 Primitive alternative rings and semisimplicity, Ann. of Math. 77 (1955), 725-730. | MR 72115 | Zbl 0066.02302
,45A generalization of commutative and alternative rings, Canad. J. Math. 22 (1970), 348-362. | MR 258896 | Zbl 0198.35503
, 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 891618 | Zbl 0631.46020
,47Complex methods and the estimations of operator norms and spectra from real numerical ranges, J. Funct. Anal. 10 (1972), 482-495. | MR 448122 | Zbl 0252.47002
,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 549296 | Zbl 0425.46037
,50An approach to numerical ranges without Banach algebra theory, Illinois, J. Math. 29 (1985), 609-635. | MR 806469 | Zbl 0604.46052
, , and ,51A general theory of Jordan rings, Proc. Nat. Acad. Sci. USA 56 (1966), 1072-1079. | MR 202783 | Zbl 0139.25502
,52The radical of a Jordan algebra, Proc. Nat. Acad. Sci. USA 62 (1969), 671-678. | MR 268238 | Zbl 0175.31002
,53On Hertein's theorems relating Jordan and associative algebras, J. Algebra 13 (1969), 382-392. | MR 249476 | Zbl 0224.16027
,54Noncommutative Jordan rings, Trans. Amer. Math. Soc. 158 (1971), 1-33. | MR 310024 | Zbl 0229.17002
,55Semisummands and semiideals in Banach spaces, Israel J. Math. 51 (1985), 33-67. | MR 804475 | Zbl 0615.46018
, and ,56Gateaux differentials in Banach algebras, Math. Z. 139 (1974), 23-34. | MR 358353 | Zbl 0275.46036
,57Jordan rings with nonzero socle, Trans. Amer. Math. Soc. 251 (1979), 375-387. | MR 531985 | Zbl 0409.17014
and ,58Noncommutative Jordan C*-algebras, Muniscripta Math. 37 (1982), 87-120. | MR 649567 | Zbl 0483.46049
, and ,59Type I factor representations of noncommutative JB*- algebras, Proc. London Math. Soc. (3) 48 (1984), 428-444. | MR 735223 | Zbl 0509.46052
, and ,60 Structure theorems for alternative H*-algebras, Math. Proc. Camb. Phil. Soc. 94 (1983), 437-446. | MR 720794 | Zbl 0551.46037
,61Banach-Jordan *-algebras, Proc. London. Math. Soc. (3) 41.(1980), 21-44. | MR 579715 | Zbl 0387.46048
and ,62A Vidav-Palmer theorem for Jordan C*-algebras and related topics, J. London Math. Soc. (2) 22 (1980), 318-332. | MR 588278 | Zbl 0483.46050
,63Non-associative normed algebras spanned by hermitian elements, Proc. London Math. Soc. (3) 47 (1983), 258-274. | MR 703979 | Zbl 0521.47036
,64The Uniqueness of the complete norm topology in complete normed nonassociative algebras, J. Funct. Anal. 60 (1985), 1-15. | MR 780101 | Zbl 0602.46055
,65C*- algebras and W*-algebras, Erg. der Math. 60, Springer-Verlag, Berlin 1971. | MR 442701 | Zbl 0219.46042
,66Generalized standard algebras, J. Algebra 12 (1969) 376-417. | MR 283035 | Zbl 0196.06102
,67Hilbert space methods in the theory of Lie algebras, Trans. Amer. Math. Soc. 95 (1960), 69-80. | MR 117575 | Zbl 0093.30601
,68 Cartan deocmposition for L*-algebras, Trans. Amer; Math. Soc. 98 (1961), 334-349. | MR 133408 | Zbl 0099.10205
,69Jordan homomorphism and derivations on a semisimple Banach algebra, Proc. Amer. Math. Soc. 24 (1970), 209-214. | MR 250069 | Zbl 0175.44001
,70 Automatic continuity of linear operators, London Math. Soc. Letc. Notes Series 21, Cambridge U. Press 1976. | MR 487371 | Zbl 0313.47029
,71The radical of an alternative ring, Ann. of Math. 49 (1948), 702-709. | MR 25449 | Zbl 0031.34501
,72The numerical range in the second dual of a Banach algebra, Math. Proc. Camb. Phil. Soc. 89 (1981), 301-307. | MR 600245 | Zbl 0461.46035
,73Power-associative regular real normed algebras, J. Austral. Math. Soc. 6 (1966), 193-209. | MR 198276 | Zbl 0145.16504
,74Symmetric Banach Manifolds and Jordan C*-algebras, North-Holland Mathematics Studies 104, Elsevier Science Publishers B.V., Amsterdam 1985. | MR 776786 | Zbl 0561.46032
,75Absolute-valued algebras, Proc. Amer. Math. Soc. 11 (1960), 861-866. | MR 120264 | Zbl 0156.03801
and ,76On the subharmonicity of the spectral radius, Boll. Un. Mat. Ital. 4 (1968), 427-429. | MR 244766
,77Hilbert space methods in the theory of Jordan algebras, Math. Proc. Camb. Phil. Soc. 78 (1974), 293-300. | Zbl 0357.17015
,78Hilbert space methods in the theory of Jordan algebras II, Math. Proc. Camb. Phil. Soc. 79 (1976), 307-319. | MR 404360 | Zbl 0357.17016
and ,79Absolute valued algebras, Proc. Nat. Acad. Sci. USA 39 (1953), 330-332. | MR 54583 | Zbl 0050.03103
,80 Jordan C*-algebras, Michigan Math. J. 24 (1977), 291-302. | MR 487478 | Zbl 0384.46040
,81 On isometries of Jordan algebras, J. London Math. Soc. (2) 17 (1978), 339-344. | MR 482212 | Zbl 0384.46041
and ,82Closed prime ideals in topological rings, Proc. London Math. Soc. 24 (1972), 307-323. | MR 298423 | Zbl 0232.46041
,83Homomorphisms on normed algebras, Pacific J. Math. 8 (1958), 373-381. | MR 104164 | Zbl 0084.33601
,84A Vidav theorem for Banach Jordan algebras, Math. Proc. Camb. Phil. Soc. 84 (1978), 263-272. | MR 493372 | Zbl 0392.46038
,85Hermitian operators on Banach Jordan algebras, Proc. Edinburgh Math. Soc. (2) 22 (1979), 93-104. | MR 549462 | Zbl 0414.46034
,86Non-unital Banach Jordan algebras and C*-triple systems, Proc. Edinburgh Math. Soc. (2) 24 (1981), 19-30. | Zbl 0441.46042
,87Coincidence of Smiley and Kleinfeld radicals in alternative rings, Algebra i Logika 8 (1969), 309-319. | MR 266972 | Zbl 0214.05201
,88A characterization of operator algebras, J. Funct. Anal. 89 (1990), 188-201. | MR 1040962 | Zbl 0714.46043
, and ,89Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006. | MR 929422 | Zbl 0691.16039
,90Structurable H*-algebras, J. Algebra (to appear). | Zbl 0749.17001
, and ,91Extended centroid and central closure of semiprime normed algebras: a first approach, Commun. Algebra 18 (1990), 2293-2326. | MR 1063136 | Zbl 0713.46033
and ,92Nonassociative ultraprime normed algebras, Quart. J. Math. Oxford (to appear). | Zbl 0758.46037
and ,93 Jordan derivations on rings, Proc. Amer; Math. Soc. 53 (1975), 321-324. | MR 399182 | Zbl 0327.16020
,94Prime nonassociative algebras, Pacific J. Math. 60 (1975), 49-63. | MR 382379 | Zbl 0355.17005
, 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 604300 | Zbl 0449.17011
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 1022011 | Zbl 0701.46027
,98 Primitive nonassociative normed algebras and extended centroid. In "Workshop on nonassociative algebraic models", Nova Science Publishers, New York (to appear). | MR 1189625 | Zbl 0941.46500
,99 Continuity of derivations on H*-algebras. Preprint 1991. | MR 1207543 | Zbl 0822.46061
,100 Rings that are nearly associative, Acadepic Press 1982. | MR 668355 | Zbl 0487.17001
, , and ,