Normal representations of Banach Jordan triple systems

Barton, T. J.; Dang, T.; Horn, G.

doi:10.1090/S0002-9939-1988-0928978-2

Normal representations of Banach Jordan triple systems
HTML articles powered by AMS MathViewer

by T. J. Barton, T. Dang and G. Horn PDF

Proc. Amer. Math. Soc. 102 (1988), 551-555 Request permission

Abstract:

Some new techniques in the representation theory of Banach Jordan triple systems (i.e., JB*-triples) are developed. These are applied to prove a Kaplansky density theorem and to show that JBW*-triples decompose into special and exceptional parts.

References

T. Barton and Richard M. Timoney, Weak$^\ast$-continuity of Jordan triple products and its applications, Math. Scand. 59 (1986), no. 2, 177–191. MR 884654, DOI 10.7146/math.scand.a-12160
Seán Dineen, Complete holomorphic vector fields on the second dual of a Banach space, Math. Scand. 59 (1986), no. 1, 131–142. MR 873493, DOI 10.7146/math.scand.a-12158
Yaakov Friedman and Bernard Russo, Structure of the predual of a $JBW^\ast$-triple, J. Reine Angew. Math. 356 (1985), 67–89. MR 779376, DOI 10.1515/crll.1985.356.67
Yaakov Friedman and Bernard Russo, The Gel′fand-Naĭmark theorem for $\textrm {JB}^\ast$-triples, Duke Math. J. 53 (1986), no. 1, 139–148. MR 835800, DOI 10.1215/S0012-7094-86-05308-1
Gilles Godefroy, Espaces de Banach: existence et unicité de certains préduaux, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 3, x, 87–105 (French, with English summary). MR 511815

Jordan operator algebras

Lawrence A. Harris, A generalization of $C^{\ast }$-algebras, Proc. London Math. Soc. (3) 42 (1981), no. 2, 331–361. MR 607306, DOI 10.1112/plms/s3-42.2.331

Klassifikation der JBW*-Tripel vom Typ

Günther Horn, Characterization of the predual and ideal structure of a $\textrm {JBW}^*$-triple, Math. Scand. 61 (1987), no. 1, 117–133. MR 929400, DOI 10.7146/math.scand.a-12194
G. Horn and E. Neher, Classification of continuous $JBW^*$-triples, Trans. Amer. Math. Soc. 306 (1988), no. 2, 553–578. MR 933306, DOI 10.1090/S0002-9947-1988-0933306-7
Wilhelm Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), no. 1, 39–64. MR 454091, DOI 10.1007/BF01360772
Wilhelm Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), no. 4, 503–529. MR 710768, DOI 10.1007/BF01173928
Wilhelm Kaup and Harald Upmeier, Jordan algebras and symmetric Siegel domains in Banach spaces, Math. Z. 157 (1977), no. 2, 179–200. MR 492414, DOI 10.1007/BF01215150
Max Koecher, An elementary approach to bounded symmetric domains, Rice University, Houston, Tex., 1969. MR 0261032
Shôichirô Sakai, $C^*$-algebras and $W^*$-algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 60, Springer-Verlag, New York-Heidelberg, 1971. MR 0442701
Harald Upmeier, Symmetric Banach manifolds and Jordan $C^\ast$-algebras, North-Holland Mathematics Studies, vol. 104, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 96. MR 776786
Jean-Pierre Vigué, Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 2, 203–281. MR 430335