Taiwanese Journal of Mathematics


B. Tabatabaie Shourijeh

Full-text: Open access


The notion of partial group $C^{*}$-algebra of a discrete group introduced by R. Exel in [3] is generalized to an idempotent unital inverse semigroup, and the partial inverse semigroup $C^{*}$-algebra is defined. By using the algebras of multipliers of ideals of an associative algebra, we can prove some theorem in the $C^{*}$-algebra context without using the approximate identity.

Article information

Taiwanese J. Math., Volume 10, Number 6 (2006), 1539-1548.

First available in Project Euclid: 18 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras

$C^{*}$-algebra partial automorphism partial Crossed product partial group $C^{*}$-algebra


Shourijeh, B. Tabatabaie. PARTIAL INVERSE SEMIGROUP $C^*$-ALGEBRA. Taiwanese J. Math. 10 (2006), no. 6, 1539--1548. doi:10.11650/twjm/1500404573. https://projecteuclid.org/euclid.twjm/1500404573

Export citation


  • R. Exel, Circle Actions on $C^{*}$-algebras, Partial Automorphisms and a Generalized Pimsner-Voiculescu Exact Sequence, J. Funct. Anal., 122 (1994), 361-401.
  • R. Exel, Twisted Partial Actions: A Classification of Regular $C^{*}$-Algebraic Bundles, Proc. London Math. Soc., 74(3) (1997), 417-443.
  • R. Exel, Partial Actions of Groups and Actions of Semigroups, Proc. Am. Math. Soc., 126(12) (1998), 3481-3494.
  • R. Exel, Associativity of Crossed Products by Partial Actions, Enveloping Actions and Partial Representation, to appear in Trans. Amr. Math. Soc.
  • J. M. G. Fell and R. S. Doran, Represnetations of $*$-Algebras, Locally Compact Groups, and Banach $*$-Algebraic Bundles, Pure and Applied Mathematics Vol. 125 and 126, Academic Press, 1988.
  • P. A. Fillmore, A User's Guide to Operator Algebras, Willey-Interscience, 1996.
  • J. M. Howie, An Introduction to Semigroup Theory, Academic Press, 1976.
  • K. McClanahan, $K$-Theory of Partial Crossed Products by Discrete Groups, J. Funct. Anal., 130 (1995), 77-117.
  • G. J. Murphy, $C^{*}$-Algebras and Operator Theory, Academic Press, Boston, 1990.
  • J. C. Quigg and I. Raeburn, Characterizations of Crossed Products by Partial Actions, J. Operator Theory, 37 (1997), 311-340.
  • N. Sieben, $C^{*}$-Crossed Products by Partial Actions and Actions of Inverse Semigroups, J. Austral. Math. Soc. $($Seris A$)$, 63 (1997), 32-46.