Hostname: page-component-5cf477f64f-n7lw4 Total loading time: 0 Render date: 2025-04-02T15:48:57.435Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak*-Closed Derivations from C[0,1] into L∞[0,1]

Published online by Cambridge University Press:  20 November 2018

Nik Weaver
Nik Weaver*
Affiliation:
Math Dept., UCLA, Los Angeles, CA 90024, USA, nweaver@math.ucla.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that every weak*-closed derivation from C[0,1] ⊂ L∞[0, 1] into L∞[0, 1] is the inverse of integration against a function in L1[0,1].

Keywords

Primary: 46L57Secondary: 46J1046E05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 3 , 01 September 1996 , pp. 367 - 375
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. K. Batty, C. J., Derivations on compact spaces, Proc. London Math. Soc. 42(1981), 299–330.Google Scholar
2. Bratteli, O., Derivations, dissipations and group actions on C*-algebras, Springer LNM 1229(1986).Google Scholar
3. Bratteli, O. and Haagerup, U., Unbounded derivations and invariant states, Commun. Math. Phys. 59( 1978), 79–95.Google Scholar
4. Bratteli, O., Herman, R. H., and Robinson, D. W., Quasianalytic vectors and derivations of operator algebras. Math. Scand. 39( 1976), 371–381.Google Scholar
5. Bratteli, O. and Robinson, D. W., Unbounded derivations of von Neumann algebras, Ann. Inst. Henri Poincaré25, Section A(1976), 139-164.Google Scholar
6. Bratteli, O. and Robinson, D. W., Unbounded derivations and invariant trace states, Commun. Math. Phys. 46( 1976), 31–35.Google Scholar
7. deLaubenfels, R., Well-behaved derivations on C[0, 1], Pac. J. Math. 115(1984), 73.Google Scholar
8. Goodman, F. M., Closed derivations in commutative C*-algebras, J. Funct. Anal. 39(1980), 308–346.Google Scholar
9. Kurose, H., An example of a non quasi well-behaved derivation in C(I), J. Funct. Anal. 43( 1981 ), 193—201.Google Scholar
10. Kurose, H., Closed derivations in C(l), Tohoku Math. J. 35(1983), 341–347.Google Scholar
11. Laczkovich, M., Derivations on differentiable functions, Real Analysis Exchange 7(1981—82), 239—254.Google Scholar
12. Sakai, S., Operator algebras in dynamical systems, Cambridge University Press, 1991.Google Scholar
13. Tomiyama, J., On the closed derivations on the unit interval, J. Ramanujan Math. Soc. 1(1986), 71—80.Google Scholar
14. Weaver, N., Order completeness in Lipschitz algebras, J. Funct. Anal. 130(1995).Google Scholar
15. Weaver, N., Nonatomic Lipschitz spaces, Studia Math. 115(1995), 277–289.Google Scholar
16. Weaver, N., Lipschitz algebras and derivations of von Neumann algebras, J. Funct. Anal., to appear.Google Scholar