摘要
Let A= （A<sub>1</sub>, …, A<sub>n</sub>） and B=（B<sub>1</sub>, …, B<sub>n</sub>） be double commuting n-tuples of operators on Hilbert space H and let L<sub>A<sub>i</sub></sub>, and R<sub>B<sub>j</sub></sub>, decode the left and right multiplications induced by A<sub>i</sub> and B<sub>j</sub>, respectively. The following results are proven: Sp （L<sub>A</sub>, R<sub>B</sub>）=Sp（A）×Sp（B）, Sp<sub>e</sub>（L<sub>A</sub>, R<sub>B</sub>）=Sp<sub>e</sub>（A）×Sp（B） ∪ Sp（A）×Sp<sub>e</sub>（B）.
Let A= (A_1, …, A_n) and B=(B_1, …, B_n) be double commuting n-tuples of operators on Hilbert space H and let L_(A_i), and R_(B_j), decode the left and right multiplications induced by A_i and B_j, respectively. The following results are proven: Sp (L_A, R_B)=Sp(A)×Sp(B), Sp_e(L_A, R_B)=Sp_e(A)×Sp(B) ∪ Sp(A)×Sp_e(B).
