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


David W. Kribs

Inductive Limit Algebras from Periodic Weighted Shifts on Fock Space

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 C*-algebras. We establish this by proving that the C*-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