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Published: |
October 13, 2002
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Keywords: |
Hilbert space, operator, weighted shift, noncommutative multivariable operator theory, Fock space, creation operators, Cuntz-Toeplitz C*-algebras, K-theory.
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Subject: |
46L05, 46L35, 47B37, 47L40.
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Abstract:
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Noncommutative multivariable versions of weighted shift operators arise
naturally as `weighted' left creation
operators acting on the Fock space Hilbert space. We identify a natural
notion
of periodicity for these $N$-tuples, and then find a family of
inductive limit
algebras determined by the periodic
weighted shifts which can be regarded as noncommutative
multivariable generalizations of
the Bunce-Deddens $\ca$-algebras. We establish this by proving that the
$\ca$-algebras generated by shifts of a given period are isomorphic to
full matrix algebras over Cuntz-Toeplitz algebras. This leads to
an isomorphism theorem which parallels the Bunce-Deddens and UHF
classification scheme.
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Acknowledgments:
Partially supported by a Canadian NSERC Post-doctoral Fellowship.
Author information:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-2068
kribs@math.purdue.edu
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