Tohoku Mathematical Journal

Some remarks on weak compactness in the dual space of a JB*-triple

Antonio M. Peralta

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Abstract

We obtain several characterizations of relatively weakly compact subsets in the predual of a JBW*-triple. As a consequence, we describe the relatively weakly compact subsets in the predual of a JBW*-algebra.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 2 (2006), 149-159.

Dates
First available in Project Euclid: 22 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1156256398

Digital Object Identifier
doi:10.2748/tmj/1156256398

Mathematical Reviews number (MathSciNet)
MR2248427

Zentralblatt MATH identifier
1126.46046

Subjects
Primary: 17C65: Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]
Secondary: 46L70: Nonassociative selfadjoint operator algebras [See also 46H70, 46K70] 46L05: General theory of $C^*$-algebras 47B99: None of the above, but in this section

Keywords
JB*-triples JB*-álgebras weak compactness

Citation

Peralta, Antonio M. Some remarks on weak compactness in the dual space of a JB*-triple. Tohoku Math. J. (2) 58 (2006), no. 2, 149--159. doi:10.2748/tmj/1156256398. https://projecteuclid.org/euclid.tmj/1156256398


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References

  • M. D. Acosta and A. M. Peralta, An alternative Dunford-Pettis property for JB*-triples, Q. J. Math. 52 (2001), 391--401.
  • C. A. Akemann, The dual space of an operator algebra, Trans. Amer. Math. Soc. 126 (1967), 286--302.
  • C. A. Akemann, P. G. Dodds and J. L. B. Gamlen, Weak compactness in the dual space of $C^* $-algebra, J. Functional Analysis 10 (1972), 446--450.
  • T. Barton and Y. Friedman, Grothendieck's inequality for JB*-triples and applications, J. London Math. Soc. (2) 36 (1987), 513--523.
  • T. Barton and Y. Friedman, Bounded derivations of JB*-triples, Quart. J. Math. Oxford Ser. (2) 41 (1990), 255--268.
  • T. Barton and R. M. Timoney, Weak*-continuity of Jordan triple products and its applications, Math. Scand. 59 (1986), 177--191.
  • J. K. Brooks, K. Saitô and J. D. M. Wright, A bounded sequence of normal functionals has a subsequence which is nearly weakly convergent, J. Math. Anal. Appl. 276 (2002), 160--167.
  • L. J. Bunce, Norm preserving extensions in JBW*-triple preduals, Q. J. Math. 52 (2001), 133--136.
  • C.-H. Chu and B. Iochum, Weakly compact operators on Jordan triples, Math. Ann. 281 (1988), 451--458.
  • C.-H. Chu and P. Mellon, The Dunford-Pettis property in JB*-triples, J. London Math. Soc. (2) 55 (1997), 515--526.
  • S. Dineen, The second dual of a JB*-triple system, Complex analysis, functional analysis and approximation theory (Campinas, 1984), 67--69, North-Holland Math. Stud. 125, North-Holland, Amsterdam, 1986.
  • C. M. Edwards, On Jordan W*-algebras, Bull. Sci. Math. (2) 104 (1980), 393--403.
  • Y. Friedman and B. Russo, Structure of the predual of a JBW*-triple, J. Reine Angew. Math. 356 (1985), 67--89.
  • H. Hanche-Olsen and E. Størmer, Jordan operator algebras, Monogr. Stud. Math. 21, Pitman, Boston Mass. 1984.
  • G. Horn, Characterization of the predual and ideal structure of a JBW$^*$-triple, Math. Scand. 61 (1987), 117--133.
  • B. Iochum, Cônes autopolaires et algebres de Jordan, Lecture Notes in Math. 1049, Springer-Verlag, Berlin, 1984.
  • H. Jarchow, Weakly compact operators on $C(K)$ and $C^*$-algebras, Functional analysis and its applications (Nice, 1986), 263--299, ICPAM Lecture Notes, World Sci. Publishing, Singapore, 1988.
  • H. Jarchow, On weakly compact operators on $C^*$-algebras, Math. Ann. 273 (1986), 341--343.
  • W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), 503--529.
  • O. Loos, Bounded symmetric domains and Jordan pairs, Math. Lectures, University of California, Irvine (1977).
  • A. M. Peralta and A. Rodríguez Palacios, Grothendieck's inequalities for real and complex $\rm JBW\sp *$-triples, Proc. London Math. Soc. (3) 83 (2001), 605--625.
  • K. Saitô, On the preduals of $W\sp* $-algebras, Tôhoku Math. J. (2) 19 (1967), 324--331.
  • S. Sakai, C*-algebras and W*-algebras, Ergeb. Math. Grenzgeb. 60, Springer-Verlag, New York-Heidelberg, 1971.
  • M. Takesaki, On the conjugate space of operator algebra, Tôhoku Math. J. (2) 10 (1958), 194--203.
  • M. Takesaki, Theory of operator algebras I, Springer-Verlag, New York-Heidelberg, 1979.
  • J. D. M. Wright, Jordan C*-algebras, Michigan Math. J. 24 (1977), 291--302.