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An invariant for unbounded operators
Author(s):
Vladimir
Manuilov;
Sergei
Silvestrov
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2593-2598.
MSC (2000):
Primary 47L60;
Secondary 19K14, 46L80
Posted:
February 17, 2006
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Abstract:
For a class of unbounded operators, a deformation of a Bott projection is used to construct an integer-valued invariant measuring deviation of the non-commutative deformations from the commutative originals, and its interpretation in terms of  -theory of  -algebras is given. Calculation of this invariant for specific important classes of unbounded operators is also presented.
References:
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- 1.
- A. Connes, N. Higson. Déformations, morphismes asymptotiques et
 -théorie bivariante. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 101-106. MR 1065438 (91m:46114) - 2.
- K. Davidson.
 -Algebras by Example. Fields Institute Monographs, AMS, 1996. MR 1402012 (97i:46095) - 3.
- G. A. Elliott, T. Natsume, R. Nest. The Heisenberg group and
 -theory.  -Theory 7 (1993), 409-428. MR 1255059 (94m:46109) - 4.
- R. Exel, T. A. Loring. Invariants of almost commuting unitaries. J. Funct. Anal. 95 (1991), 364-376. MR 1092131 (92a:46083)
- 5.
- V. M. Manuilov. An invariant for pairs of almost commuting unbounded operators. Funktsional. Anal. i Prilozhen. 32 (1998), No. 4, 88-91 (in Russian). English translation: Functional Anal. Appl. 32 (1998), 288-291. MR 1678864 (99m:47030)
- 6.
- D. Voiculescu. Asymptotically commuting finite rank unitary operators without commuting approximants. Acta Sci. Math. (Szeged) 45 (1983), 429-431. MR 0708811 (85d:47035)
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Additional Information:
Vladimir
Manuilov
Affiliation:
Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
Email:
manuilov@mech.math.msu.su
Sergei
Silvestrov
Affiliation:
Department of Mathematics, Centre for Mathematical Sciences, Lund Institute of Technology, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
Email:
sergei.silvestrov@math.lth.se
DOI:
10.1090/S0002-9939-06-08284-0
PII:
S 0002-9939(06)08284-0
Keywords:
Bott projections,
$K$-group,
deformations,
invariant
Received by editor(s):
October 7, 2004
Received by editor(s) in revised form:
March 21, 2005
Posted:
February 17, 2006
Additional Notes:
The first author was supported in part by the RFFI grant No.~05-01-00923 and H\Russian{Sh}-619.2003.01, and the second author by the Crafoord Foundation, the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) and the Royal Swedish Academy of Sciences. Part of this research was performed during the \mbox{Non-commutative} Geometry program 2003/2004, Mittag-Leffler Institute, Stockholm.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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