Tensor products and joint spectra for solvable Lie algebras of operators

Autores: Enrico Boasso
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 1, 1998, págs. 9-16
Idioma: inglés
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Resumen
- 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 $Sp(L_2,H_2)$.