Tensor products and joint spectra for solvable Lie algebras of operators (Q1366594)

Given two complex Hilbert spaces, \(H_1\) and \(H_2\), and two complex solvable finite-dimensional Lie algebras of operators, \(L_1\) and \(L_2\), such that \(L_i\) acts on \(H_i\), \(i=1,2\), the joint spectrum of the Lie algebra \(L_1\times L_2\), which acts on \(H_1\overline{\otimes} H_2\), is expressed by the cartesian product of \(Sp(L_1,H_1)\), and \(Sp(L_2,H_2)\).