The C*-algebra of a partial isometry

Authors:
Berndt Brenken and Zhuang Niu

Journal:
Proc. Amer. Math. Soc. **140** (2012), 199-206

MSC (2010):
Primary 46L35, 46L80, 47C15

Published electronically:
May 11, 2011

MathSciNet review:
2833532

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The universal C*-algebra generated by a partial isometry is a non-unital residually finite dimensional C*-algebra which is not exact. Many unitarily inequivalent partial isometries generating any given finite dimensional full matrix algebra are constructed. The -groups of this algebra are computed, and it is shown that all projections in the algebra are equivalent.

**[B]**B. Blackadar,*Operator algebras*, Encyclopaedia of Mathematical Sciences, vol. 122, Springer-Verlag, Berlin, 2006. Theory of 𝐶*-algebras and von Neumann algebras; Operator Algebras and Non-commutative Geometry, III. MR**2188261****[Ch]**Man Duen Choi,*The full 𝐶*-algebra of the free group on two generators*, Pacific J. Math.**87**(1980), no. 1, 41–48. MR**590864****[HM]**P. R. Halmos and J. E. McLaughlin,*Partial isometries*, Pacific J. Math.**13**(1963), 585–596. MR**0157241****[KR]**Richard V. Kadison and John R. Ringrose,*Fundamentals of the theory of operator algebras. Vol. I*, Pure and Applied Mathematics, vol. 100, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. Elementary theory. MR**719020****[OZ]**Catherine L. Olsen and William R. Zame,*Some 𝐶*-alegebras with a single generator*, Trans. Amer. Math. Soc.**215**(1976), 205–217. MR**0388114**, 10.1090/S0002-9947-1976-0388114-7**[P]**Carl Pearcy,*On certain von Neumann algebras which are generated by partial isometries*, Proc. Amer. Math. Soc.**15**(1964), 393–395. MR**0161172**, 10.1090/S0002-9939-1964-0161172-8**[R]**Iain Raeburn,*Graph algebras*, CBMS Regional Conference Series in Mathematics, vol. 103, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2005. MR**2135030****[T]**Masamichi Takesaki,*Theory of operator algebras. I*, Springer-Verlag, New York-Heidelberg, 1979. MR**548728**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2010):
46L35,
46L80,
47C15

Retrieve articles in all journals with MSC (2010): 46L35, 46L80, 47C15

Additional Information

**Berndt Brenken**

Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada

**Zhuang Niu**

Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NL A1C 5S7, Canada

DOI:
http://dx.doi.org/10.1090/S0002-9939-2011-10988-2

Received by editor(s):
October 1, 2009

Received by editor(s) in revised form:
November 3, 2010

Published electronically:
May 11, 2011

Communicated by:
Marius Junge

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.