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Transactions of the American Mathematical Society

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Geometric aspects of multiparameter spectral theory


Authors: Luzius Grunenfelder and Tomaž Košir
Journal: Trans. Amer. Math. Soc. 350 (1998), 2525-2546
MSC (1991): Primary 13H15, 14C17, 15A54
DOI: https://doi.org/10.1090/S0002-9947-98-02078-9
MathSciNet review: 1451601
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Abstract: 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: luzius@cs.dal.ca

Tomaž Košir
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: tomaz.kosir@fmf.uni-lj.si

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.
Article copyright: © Copyright 1998 American Mathematical Society