Derivations in Commutative C*-Algebras

  • H. Kurose
Part of the Progress in Mathematics book series (PM, volume 84)


Prof. S. Sakai began the systematic study of unbounded *-derivations in C*-algebras after his work on bounded *-derivations. For the theory of the unbounded *-derivations, he posed many questions in his lecture notes and his talks ([SI, S2]). In the case of commutative C*-algebras, several authors have developed the theory by trying to solve his problems ([Ba], [G]). In consequence, roughly speaking, now we may say that the structure of closed *-derivations has been almost clarified when the underlying space of the commutative C*-algebra is of 0- or 1-dimension, though a few problems have been left unsolved. Furthermore the structure of *-derivations commuting with group actions has rapidly become clear in the last decade. In this note, we shall not mention these structures, using as our references [Bra] and [T].


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  1. [Ba]
    C.J.K. Batty, Derivations on compact spaces, Proc. London Math. Soc. 42 (1981), 299–330.MathSciNetMATHCrossRefGoogle Scholar
  2. [Bra]
    O. Bratteli, Dissipations and Group Actions on C*-Algebras, Springer Lecture Notes in Math., 1229 (1986).Google Scholar
  3. [G]
    F.M. Goodman, Closed derivations in commutative C*-algebras, J. Funct. Anal. 39 (1980), 308–346.MathSciNetMATHCrossRefGoogle Scholar
  4. [K]
    H. Kurose, Closed derivations on compact spaces, J. London Math. Soc. 34 (1986), 524–533.MathSciNetMATHCrossRefGoogle Scholar
  5. [Ni]
    K. Nishio, A local kernel property of closed derivations on C(I × I), Proc. Amer. Math. Soc. 95 (1985), 573–576.MathSciNetMATHGoogle Scholar
  6. [SI]
    S. Sakai, Theory of Unbounded Derivations in C*-Algebras, Lecture Notes, Copenhagen Univ. and Univ. of Newcastle upon Tyne, 1977.Google Scholar
  7. [S2]
    S. Sakai, Development in the theory of unbounded derivations in C*algebras, Symposia in Pure Mathematics Vol. 38, Providence, R.I., 1982, 309–331.Google Scholar
  8. [T]
    J. Tomiyama, The Theory of Closed Derivations in the Algebra of Continuous Functions on the Unit Interval, Lecture Notes, Tsing Hua Univ., 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • H. Kurose
    • 1
  1. 1.Department of Applied MathematicsFukuoka UniversityFukuokaJapan

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