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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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