[1] E. M. Alfsen, H. Hanche-Olsen and F. W. Schultz, State spaces of C∗-algebras,
Acta Math. 144 (1980) 267–305.
[2] D. P. Blecher and C. Le Merdy, Operator algebras and their modules—an operator
space approach, London Mathematical Society Monographs. New Series,
vol. 30, The Clarendon Press Oxford University Press, Oxford (2004), oxford
Science Publications.
[3] L. J. Bunce, B. Feely and R. M. Timoney, Operator space struc-
ture of JC∗-triples and TROs, I, Math. Z. 270 (2012) 961–982, URL
http://dx.doi.org/10.1007/s00209-010-0834-y.
[4] L. J. Bunce and R. M. Timoney, On the operator space structure
of Hilbert spaces, Bull. Lond. Math. Soc. 43 (2011) 1205–1218, URL
http://dx.doi.org/10.1112/blms/bdr054.
[5] —, On the universal TRO of a JC∗-triple, ideals, and tensor products, Quart.
J. Math. (to appear) (2012).
[6] P. M. Cohn, On homomorphic images of special Jordan algebras, Canadian J.
Math. 6 (1954) 253–264.
[7] C. M. Edwards and G. T. R¨uttimann, On the facial structure of the unit balls
in a JBW∗-triple and its predual, J. London Math. Soc. (2) 38 (1988) 317–332,
URL http://dx.doi.org/10.1112/jlms/s2-38.2.317.
[8] —, Peirce inner ideals in Jordan∗-triples, J. Algebra 180 (1996) 41–66.
[9] E. G. Effros, N. Ozawa and Z.-J. Ruan, On injectivity and nuclearity for op-
erator spaces, Duke Math. J. 110 (2001) 489–521.
28 L. J. BUNCE AND R. M. TIMONEY
[10] E. G. Effros and Z.-J. Ruan, Operator spaces, London Mathematical Soci-
ety Monographs. New Series, vol. 23, The Clarendon Press Oxford University
Press, New York (2000).
[11] E. G. Effros and E. Størmer, Positive projections and Jordan structure in
operator algebras, Math. Scand. 45 (1979) 127–138.
[12] Y. Friedman and B. Russo, Solution of the contractive pro-
jection problem, J. Funct. Anal. 60 (1985) 56–79, URL
http://dx.doi.org/10.1016/0022-1236(85)90058-8.
[13] —, The Gel′fand-Na˘ımark theorem for JB∗-triples, Duke Math. J. 53 (1986)
139–148.
[14] M. Hamana, Triple envelopes and ˇSilov boundaries of operator spaces, Math.
J. Toyama Univ. 22 (1999) 77–93.
[15] H. Hanche-Olsen, On the structure and tensor products of JC-algebras, Canad.
J. Math. 35 (1983) 1059–1074.
[16] H. Hanche-Olsen and E. Størmer, Jordan operator algebras, Monographs and
Studies in Mathematics, vol. 21, Pitman (Advanced Publishing Program),
Boston, MA (1984).
[17] L. A. Harris, Bounded symmetric homogeneous domains in infinite dimensional
spaces, in Proceedings on Infinite Dimensional Holomorphy (Internat. Conf.,
Univ. Kentucky, Lexington, Ky., 1973), Springer, Berlin, pp. 13–40. Lecture
Notes in Math., Vol. 364.
[18] —, A generalization of C∗-algebras, Proc. London Math. Soc. (3) 42 (1981)
331–361.
[19] G. Horn, Characterization of the predual and ideal structure of a JBW∗-triple,
Math. Scand. 61 (1987) 117–133.
[20] —, Classification of JBW∗-triples of type I, Math. Z. 196 (1987) 271–291.
[21] G. Horn and E. Neher, Classification of continuous JBW∗-triples, Trans.
Amer. Math. Soc. 306 (1988) 553–578.
[22] R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator
algebras. Vol. II, Graduate Studies in Mathematics, vol. 16, American Mathematical
Society, Providence, RI (1997), advanced theory, Corrected reprint of
the 1986 original.
[23] W. Kaup, A Riemann mapping theorem for bounded symmetric domains in
complex Banach spaces, Math. Z. 183 (1983) 503–529.
[24] —, On JB∗-triples defined by fibre bundles, Manuscripta Math. 87 (1995) 379–
403.
[25] M. Neal, ´E. Ricard and B. Russo, Classification of contractively complemented
Hilbertian operator spaces, J. Funct. Anal. 237 (2006) 589–616.
[26] M. Neal and B. Russo, Contractive projections and operator spaces, Trans.
Amer. Math. Soc. 355 (2003) 2223–2262 (electronic).
[27] —, Operator space characterizations of C∗-algebras and ternary rings, Pacific
J. Math. 209 (2003) 339–364.
[28] —, Representation of contractively complemented Hilbertian operator spaces on
the Fock space, Proc. Amer. Math. Soc. 134 (2006) 475–485 (electronic).
[29] ´ A. Rodr´ıguez-Palacios, Jordan structures in analysis, in Jordan algebras
(Oberwolfach, 1992), de Gruyter, Berlin (1994) pp. 97–186.
[30] B. Russo, Structure of JB∗-triples, in Jordan algebras (Oberwolfach, 1992), de
Gruyter, Berlin (1994) pp. 209–280.
[31] P. J. Stacey, The structure of type I JBW-algebras, Math.
Proc. Cambridge Philos. Soc. 90 (1981) 477–482, URL
http://dx.doi.org/10.1017/S030500410005893X.
[32] —, Type I2 JBW-algebras, Quart. J. Math. Oxford Ser. (2) 33 (1982) 115–127.
UNIVERSALLY REVERSIBLE JC�-TRIPLES AND OPERATOR SPACES 29
[33] M. Takesaki, Theory of operator algebras. I, Springer-Verlag, New York (1979).
[34] D. M. Topping, Jordan algebras of self-adjoint operators, Mem. Amer. Math.
Soc. No. 53 (1965) 48.
[35] H. Zettl, A characterization of ternary rings of operators, Adv. in Math. 48
(1983) 117–143.
Department of Mathematics, University of Reading, Reading RG6
2AX
E-mail address: l.j.bunce@reading.ac.uk
School of Mathematics, Trinity College, Dublin 2
E-mail address: richardt@maths.tcd.ie
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