Bicircular projections and characterization of Hilbert spaces
HTML articles powered by AMS MathViewer
- by László L. Stachó and Borut Zalar
- Proc. Amer. Math. Soc. 132 (2004), 3019-3025
- DOI: https://doi.org/10.1090/S0002-9939-04-07333-2
- Published electronically: June 2, 2004
- PDF | 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
Bibliographic Information
- László L. Stachó
- Affiliation: University of Szeged, Bolyai Institute, Aradi Vértanúk tere 1, 6720 Szeged, Hungary
- Email: stacho@math.u-szeged.hu
- Borut Zalar
- Affiliation: University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
- Email: borut.zalar@uni-mb.si
- Received by editor(s): February 19, 2002
- Received by editor(s) in revised form: March 26, 2003
- Published electronically: June 2, 2004
- Communicated by: David R. Larson
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3019-3025
- MSC (2000): Primary 47L70; Secondary 17C65
- DOI: https://doi.org/10.1090/S0002-9939-04-07333-2
- MathSciNet review: 2063123