| 关于一个次可乘定理 |
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| 引用本文： | 吴畏.关于一个次可乘定理[J].数学学报,1999,42(5):877-882. |
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| 作者姓名： | 吴畏 |
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| 作者单位： | 中国科学院数学研究所,北京,100080 |
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| 摘 要： | 本文证明了次可乘定理：设A是一个*代数，A上范数||.||使得（A，||.||）成为完备的赋范线性空间，而且，（I）对于X∈A,||x*x||||x||2；（II）对于正规元x∈A,||x*x||=||x||2，则（A，||.||）是C*-代数．同时，也给出了其对应的C*-等价定理．
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| 关 键 词： | C~*-代数 正规元 C~*-等价 次可乘 |
| 修稿时间： | :1997-12-1 |
On a Theorem of Submultiplication |
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| Wu Wei.On a Theorem of Submultiplication[J].Acta Mathematica Sinica,1999,42(5):877-882. |
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| Authors: | Wu Wei |
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| Institution: | Wu Wei (Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China)(E-mail: wwu@moth03 .math. ac. cn) |
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| Abstract: | In this paper, we present a complete proof of a theorem of submultiplication which claims that a*-algebra A with complete linear space norm such that ||x*x|| ||x||2 for x ∈ A and ||x*x|| = ||x||2 for normal ∈ E A is a C*-algebra. At the same time,a C*-equivalent version of the theorem is given. |
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| Keywords: | ?C*-algebra Normal element C*-equivalent Submultiplication |
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