On 𝐽𝐵*-triples which are M-ideals in their biduals

Cabello, Juan; Nieto, Eduardo

doi:10.1090/S0002-9939-98-04434-7

On $JB^*$-triples which are M-ideals in their biduals
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by Juan Carlos Cabello and Eduardo Nieto PDF

Proc. Amer. Math. Soc. 126 (1998), 2277-2283 Request permission

Abstract:

The object of this paper is to investigate $JB^*$-triples which are M-ideals in their biduals.

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
Ehrhard Behrends, $M$-structure and the Banach-Stone theorem, Lecture Notes in Mathematics, vol. 736, Springer, Berlin, 1979. MR 547509, DOI 10.1007/BFb0063153
J. C. Cabello, Containing of $l_{1}$ or $c_{0}$ and the best approximation. Collect. Math. 41, 3 (1990) 233-241.
J. C. Cabello and E. Nieto, On properties of M-ideals. To appear in Rocky Mountain J. Math.
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
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
G. Godefroy and N. J. Kalton, The ball topology and its applications, Banach space theory (Iowa City, IA, 1987) Contemp. Math., vol. 85, Amer. Math. Soc., Providence, RI, 1989, pp. 195–237. MR 983386, DOI 10.1090/conm/085/983386
G. Godefroy, N. J. Kalton, and P. D. Saphar, Unconditional ideals in Banach spaces, Studia Math. 104 (1993), no. 1, 13–59. MR 1208038
G. Godefroy and D. Li, Banach spaces which are $M$-ideals in their bidual have property $(\textrm {u})$, Ann. Inst. Fourier (Grenoble) 39 (1989), no. 2, 361–371 (English, with French summary). MR 1017283, DOI 10.5802/aif.1170
Gilles Godefroy and Paulette Saab, Quelques espaces de Banach ayant les propriétés (V) ou (V$^\ast$) de A. Pełczyński, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 11, 503–506 (French, with English summary). MR 865871
Peter Harmand and Åsvald Lima, Banach spaces which are $M$-ideals in their biduals, Trans. Amer. Math. Soc. 283 (1984), no. 1, 253–264. MR 735420, DOI 10.1090/S0002-9947-1984-0735420-4
P. Harmand, D. Werner, and W. Werner, $M$-ideals in Banach spaces and Banach algebras, Lecture Notes in Mathematics, vol. 1547, Springer-Verlag, Berlin, 1993. MR 1238713, DOI 10.1007/BFb0084355
Daniel Li, Espaces $L$-facteurs de leurs biduaux: bonne disposition, meilleure approximation et propriété de Radon-Nikodým, Quart. J. Math. Oxford Ser. (2) 38 (1987), no. 150, 229–243 (French, with English summary). MR 891618, DOI 10.1093/qmath/38.2.229
Åsvald Lima, On $M$-ideals and best approximation, Indiana Univ. Math. J. 31 (1982), no. 1, 27–36. MR 642613, DOI 10.1512/iumj.1982.31.31004
Rafael Payá, Javier Pérez, and Angel Rodríguez, Noncommutative Jordan $C^{\ast }$-algebras, Manuscripta Math. 37 (1982), no. 1, 87–120. MR 649567, DOI 10.1007/BF01239948
Rafael Payá and David Yost, The two-ball property: transitivity and examples, Mathematika 35 (1988), no. 2, 190–197. MR 986628, DOI 10.1112/S0025579300015187
David Yost, The $n$-ball properties in real and complex Banach spaces, Math. Scand. 50 (1982), no. 1, 100–110. MR 664511, DOI 10.7146/math.scand.a-11947