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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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$C^\ast$-algebras generated by a subnormal operator
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by Kit C. Chan and Z̆eljko C̆uc̆ković PDF
Trans. Amer. Math. Soc. 351 (1999), 1445-1460 Request permission


Using the functional calculus for a normal operator, we provide a result for generalized Toeplitz operators, analogous to the theorem of Axler and Shields on harmonic extensions of the disc algebra. Besides that result, we prove that if $T$ is an injective subnormal weighted shift, then any two nontrivial subspaces invariant under $T$ cannot be orthogonal to each other. Then we show that the $C^*$-algebra generated by $T$ and the identity operator contains all the compact operators as its commutator ideal, and we give a characterization of that $C^*$-algebra in terms of generalized Toeplitz operators. Motivated by these results, we further obtain their several-variable analogues, which generalize and unify Coburn’s theorems for the Hardy space and the Bergman space of the unit ball.
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Additional Information
  • Kit C. Chan
  • Affiliation: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221
  • Email:
  • Z̆eljko C̆uc̆ković
  • Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606-3390
  • MR Author ID: 294593
  • Email:
  • Received by editor(s): December 4, 1995
  • Received by editor(s) in revised form: March 4, 1998
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1445-1460
  • MSC (1991): Primary 47B20, 32A37, 46L05; Secondary 46E20, 47A13, 47B37
  • DOI:
  • MathSciNet review: 1624093