| ON THE TAYLOR'S JOINT SPECTRUM OF 2n-TUPLE (L_A, R_B) |
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| 引用本文： | Li Shaokuan,Ji Yao. ON THE TAYLOR'S JOINT SPECTRUM OF 2n-TUPLE (L_A, R_B)[J]. 数学年刊B辑(英文版), 1989, 10(1): 33-37 |
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| 作者姓名： | Li Shaokuan Ji Yao |
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| 作者单位： | China Textile University Shanghai China，China Textile University Shanghai China |
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| 摘 要： | 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).
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| 收稿时间： | 1986-04-01 |
ON THE TAYLOR''S JOINT SPECTRUM OF 2n-TUPLE($L_{A},R_{B}$) |
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| Li Shaokuan and Ji Yao. ON THE TAYLOR''S JOINT SPECTRUM OF 2n-TUPLE($L_{A},R_{B}$)[J]. Chinese Annals of Mathematics,Series B, 1989, 10(1): 33-37 |
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| Authors: | Li Shaokuan and Ji Yao |
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| Affiliation: | China Textile University, Shanghai,China. |
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| Abstract: | Let $[A = ({A_1}, cdots ,{A_n})]$ and $[B = ({B_1}, cdots {B_n})]$ be double commuting n-tuples of operatorson Hilbert space H and let $[{L_{{A_i}}}]$ and $[{R_{{B_j}}}]$ denote the left and right multiplications induced by$[{A_i}]$ and $[{B_j}]$ respectively. The following results are proven: $$[{S_p}({L_{A,}}{R_B}) = {S_p}(A) times {S_p}(B),{S_{{p_e}}}({L_A},{R_B}) = {S_{{p_e}}}(A) times {S_p}(B) cup {S_p}(A) times {S_{{p_e}}}(B).]$$ |
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