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 e-prints
- Pub Date:
- January 2016
- DOI:
- 10.48550/arXiv.1601.02122
- arXiv:
- arXiv:1601.02122
- Bibcode:
- 2016arXiv160102122B
- Keywords:
-
- Mathematics - Functional Analysis;
- Primary 47A13;
- 17B30;
- Secondary 46M05;
- 47A80
- E-Print:
- 7 pages, original research article