Spectral properties of tensor products of linear operators. I
Takashi Ichinose · Transactions of the American Mathematical Society · 1978
The aim of the present paper is to obtain, for tensor products of linear operators, their essential spectra in the sense of F. E. Browder, F. Wolf and M. Schechter and explicit formulae of their nullity, deficiency and index. The theory applies to $A \otimes I + I \otimes B$ and $A \otimes B$.