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Published: 
October 13, 2002

Keywords: 
Hilbert space, operator, weighted shift, noncommutative multivariable operator theory, Fock space, creation operators, CuntzToeplitz C*algebras, Ktheory.

Subject: 
46L05, 46L35, 47B37, 47L40.

Abstract:

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 BunceDeddens $\ca$algebras. We establish this by proving that the
$\ca$algebras generated by shifts of a given period are isomorphic to
full matrix algebras over CuntzToeplitz algebras. This leads to
an isomorphism theorem which parallels the BunceDeddens and UHF
classification scheme.

Acknowledgments:
Partially supported by a Canadian NSERC Postdoctoral Fellowship.
Author information:
Department of Mathematics, Purdue University, West Lafayette, IN 479072068
kribs@math.purdue.edu
 