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On the spectral set of a solvable Lie algebra of operators. (English) Zbl 0891.47005
Summary: If $$L$$ is a complex solvable finite-dimensional Lie algebra of operators acting on a Banach space $$E$$, and $$\{x_i\}_{1\leq i\leq n}$$ is a Jordan-Hölder basis of $$L$$, we study the relation between $$\text{Sp}(L,E)$$ and $$\prod \text{Sp}(x_i)$$, when $$L$$ is a nilpotent or a solvable Lie algebra.
##### MSC:
 47A13 Several-variable operator theory (spectral, Fredholm, etc.) 17B30 Solvable, nilpotent (super)algebras 17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
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