Geometric aspects of multiparameter spectral theory

Grunenfelder, Luzius; Košir, Tomaž

doi:10.1090/S0002-9947-98-02078-9

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

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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