Bicircular projections and characterization of Hilbert spaces

Stachó, László; Zalar, Borut

doi:10.1090/S0002-9939-04-07333-2

Bicircular projections and characterization of Hilbert spaces
HTML articles powered by AMS MathViewer

by László L. Stachó and Borut Zalar PDF

Proc. Amer. Math. Soc. 132 (2004), 3019-3025 Request permission

Abstract:

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

References

L. J. Bunce and C.-H. Chu, Compact operations, multipliers and Radon-Nikodým property in $\textrm {JB}^*$-triples, Pacific J. Math. 153 (1992), no. 2, 249–265. MR 1151560, DOI 10.2140/pjm.1992.153.249
L. J. Bunce, C.-H. Chu, L. L. Stachó, and B. Zalar, On prime $\textrm {JB}^*$-triples, Quart. J. Math. Oxford Ser. (2) 49 (1998), no. 195, 279–290. MR 1645548, DOI 10.1093/qjmath/49.195.279
C.-H. Chu and P. Mellon, The Dunford-Pettis property in $\textrm {JB}^*$-triples, J. London Math. Soc. (2) 55 (1997), no. 3, 515–526. MR 1452262, DOI 10.1112/S002461079700522X
Seán Dineen, The Schwarz lemma, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1989. Oxford Science Publications. MR 1033739
C. M. Edwards and G. T. Rüttimann, On the facial structure of the unit balls in a $\textrm {JBW}^*$-triple and its predual, J. London Math. Soc. (2) 38 (1988), no. 2, 317–332. MR 966303, DOI 10.1112/jlms/s2-38.2.317
Yaakov Friedman and Bernard Russo, Solution of the contractive projection problem, J. Funct. Anal. 60 (1985), no. 1, 56–79. MR 780104, DOI 10.1016/0022-1236(85)90058-8
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
Yaakov Friedman and Bernard Russo, Conditional expectation and bicontractive projections on Jordan $C^\ast$-algebras and their generalizations, Math. Z. 194 (1987), no. 2, 227–236. MR 876232, DOI 10.1007/BF01161970
Günther Horn, Classification of JBW$^*$-triples of type $\textrm {I}$, Math. Z. 196 (1987), no. 2, 271–291. MR 910832, DOI 10.1007/BF01163661
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
José-M. Isidro and Wilhelm Kaup, Determining boundary sets of bounded symmetric domains, Manuscripta Math. 81 (1993), no. 1-2, 149–159. MR 1247595, DOI 10.1007/BF02567851
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, Contractive projections on Jordan $C^{\ast }$-algebras and generalizations, Math. Scand. 54 (1984), no. 1, 95–100. MR 753066, DOI 10.7146/math.scand.a-12043
Ottmar Loos, Jordan pairs, Lecture Notes in Mathematics, Vol. 460, Springer-Verlag, Berlin-New York, 1975. MR 0444721, DOI 10.1007/BFb0080843
Á. Rodríguez-Palacios, On the strong${}^*$ topology of a $\textrm {JBW}^*$-triple, Quart. J. Math. Oxford Ser. (2) 42 (1991), no. 165, 99–103. MR 1094345, DOI 10.1093/qmath/42.1.99
Bernard Russo, Structure of $\textrm {JB}^*$-triples, Jordan algebras (Oberwolfach, 1992) de Gruyter, Berlin, 1994, pp. 209–280. MR 1293321
L. L. Stachó, A projection principle concerning biholomorphic automorphisms, Acta Sci. Math. (Szeged) 44 (1982), no. 1-2, 99–124. MR 660517
L. L. Stachó and B. Zalar, Symmetric continuous Reinhardt domains, Arch. Math. (Basel) 81 (2003), 50-61.
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