Tensor products and joint spectra for solvable Lie algebras of operators
Abstract
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 $Sp(L_2,H_2)$.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.02122
 Bibcode:
 2016arXiv160102122B
 Keywords:

 Mathematics  Functional Analysis;
 Primary 47A13;
 17B30;
 Secondary 46M05;
 47A80
 EPrint:
 7 pages, original research article