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New York Journal of Mathematics 8 (2002), 145-159.

Inductive limit algebras from periodic weighted shifts on Fock space

David W. Kribs

Published: October 13, 2002
Keywords: Hilbert space, operator, weighted shift, noncommutative multivariable operator theory, Fock space, creation operators, Cuntz-Toeplitz C*-algebras, K-theory.
Subject: 46L05, 46L35, 47B37, 47L40.


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.

Partially supported by a Canadian NSERC Post-doctoral Fellowship.

Author information:
Department of Mathematics, Purdue University, West Lafayette, IN 47907-2068