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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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Geometric aspects of multiparameter spectral theory
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by Luzius Grunenfelder and Tomaž Košir PDF
Trans. Amer. Math. Soc. 350 (1998), 2525-2546 Request permission


The paper contains a geometric description of the dimension of the total root subspace of a regular multiparameter system in terms of the intersection multiplicities of its determinantal hypersurfaces. The new definition of regularity used here is proved to restrict to the familiar definition in the linear case. A decomposability problem is also considered. It is shown that the joint root subspace of a multiparameter system may be decomposable even when the root subspace of each member is indecomposable.
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Additional Information
  • Luzius Grunenfelder
  • Affiliation: Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5
  • Email:
  • Tomaž Košir
  • Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
  • Email:
  • Received by editor(s): September 26, 1996
  • Additional Notes: Research supported in part by the NSERC of Canada and by the Ministry of Science and Technology of Slovenia.
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2525-2546
  • MSC (1991): Primary 13H15, 14C17, 15A54
  • DOI:
  • MathSciNet review: 1451601