| 弱闭T(N)-模的预零化子的等距映射 |
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| 引用本文： | 骆建文,陆芳言.弱闭T(N)-模的预零化子的等距映射[J].数学学报,2003,46(1):131-136. |
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| 作者姓名： | 骆建文 陆芳言 |
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| 作者单位： | 1. 上海交通大学管理学院,上海,200052
2. 苏州大学数学系,江苏,215006 |
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| 基金项目： | 国家自然科学基金资助项目(19971072) |
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| 摘 要： | 本文刻划了弱闭T(N)-模的预零化子间的等距映射.设u,W分别为由左连续序同态N→~N和N→~N所确定的弱闭T(N)-模, u(?),W(?)分别为u,W的预零化子,Φ为由u(?)到W(?)上的线性等距映射.若(0)*=(0)#=(0),dim(0)+≠1且min{dim(H(?)~H),dim(He(?)^H)}≥2,则存在酉算子Ui,Vi(i=1,2),使得Φ(A)=U1AV*1或Φ(A)=U2A*V2*.
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| 关 键 词： | 套代数 弱闭T(N)-模 预零化子 等距映射 |
| 文章编号： | 0583-1431(2003)01-0131-06 |
| 修稿时间： | 2000年6月5日 |
Isometries of the Preannihilators of Weakly Closed T(N)-Modules |
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| Jian Wen LUO.Isometries of the Preannihilators of Weakly Closed T(N)-Modules[J].Acta Mathematica Sinica,2003,46(1):131-136. |
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| Authors: | Jian Wen LUO |
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| Institution: | Jian Wen LUO (School of Management, Shanghai Jiaotong University, Shanghai 200052, P. R. China)Fang Yan LU (Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China) |
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| Abstract: | In this paper, we characterize the linear surjective isometrics between the preannihilators of weakly closed T(N)-modules. Let U and W be the weakly closed T(N)-modules determined by the left order homomorphisms N → N and N→N respectively, and let U(?) and W(?) be the preannihilators of U and W on a Hilbert space H respectively. We prove that the onto isometrics between the spaces U(?) and W(?) are of the form A→U1AV1* or A → U2A*V2, where Ui and Vi (i = 1,2) are unitary operators, if (0)* = (0)# = (0), dim(0)+ ≠ 1 and min{dim(H(?)H), dim(H(?) H)} ≥ 2. |
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| Keywords: | Nest algebras Weakly closed T(N)-Modules Preannihilators Isometries |
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