The C*algebra of a partial isometry
Authors:
Berndt Brenken and Zhuang Niu
Journal:
Proc. Amer. Math. Soc. 140 (2012), 199206
MSC (2010):
Primary 46L35, 46L80, 47C15
Published electronically:
May 11, 2011
MathSciNet review:
2833532
Fulltext PDF
Abstract 
References 
Similar Articles 
Additional Information
Abstract: The universal C*algebra generated by a partial isometry is a nonunital 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, SpringerVerlag, Berlin, 2006. Theory of
𝐶*algebras and von Neumann algebras; Operator Algebras and
Noncommutative Geometry, III. MR 2188261
(2006k:46082)
 [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 (82b:46069)
 [HM]
P.
R. Halmos and J.
E. McLaughlin, Partial isometries, Pacific J. Math.
13 (1963), 585–596. MR 0157241
(28 #477)
 [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
(85j:46099)
 [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
(52 #8951), 10.1090/S00029947197603881147
 [P]
Carl
Pearcy, On certain von Neumann algebras which
are generated by partial isometries, Proc.
Amer. Math. Soc. 15
(1964), 393–395. MR 0161172
(28 #4380), 10.1090/S00029939196401611728
 [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
(2005k:46141)
 [T]
Masamichi
Takesaki, Theory of operator algebras. I, SpringerVerlag, New
YorkHeidelberg, 1979. MR 548728
(81e:46038)
 [B]
 B. Blackadar, Theory of C*algebras and von Neumann Algebras, Encyclopaedia of Mathematical Sciences, 122. Operator Algebras and Noncommutative Geometry 7, SpringerVerlag, Berlin, 2006. MR 2188261 (2006k:46082)
 [Ch]
 M.D. Choi, The full C*algebra of the free group on two generators, Pacific J. Math. 87 (1980), 4148. MR 590864 (82b:46069)
 [HM]
 P. R. Halmos, J. E. McLaughlin, Partial isometries, Pacific J. Math. 13 (1963), 585596. MR 0157241 (28:477)
 [KR]
 R. V. Kadison, J. Ringrose, Fundamentals of the Theory of Operator Algebras, Vol. I, Academic Press, New York, 1983. MR 719020 (85j:46099)
 [OZ]
 C. Olsen, W. Zame, Some C*algebras with a single generator, Trans. Amer. Math. Soc. 215 (1976), 205217. MR 0388114 (52:8951)
 [P]
 C. Pearcy, On certain Von Neumann algebras which are generated by partial isometries, Proc. Amer. Math. Soc. 15, No. 3 (1964), 393395. MR 0161172 (28:4380)
 [R]
 I. Raeburn, Graph Algebras, CBMS Regional Conference Series in Math., vol. 103, AMS, Providence, Rhode Island, 2005. MR 2135030 (2005k:46141)
 [T]
 M. Takesaki, Theory of Operator Algebras, SpringerVerlag, New York, 1979. MR 548728 (81e:46038)
Similar Articles
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/S000299392011109882
PII:
S 00029939(2011)109882
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.
