| THE CODIMENSION FORMULA ON AF－COSUBMODULES |
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| 作者姓名： | GUO Kunyu |
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| 作者单位： | GUO KUNYU Department of Mathematics,Fudan University,Shanghai 200433,China |
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| 基金项目： | National Natural Science Foundation of China(No.10171019),Shuguan Project Shanghai and the Young Teacher Fund of Higher School of the Ministry of Education of China |
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| 摘 要： | Let M_1,M_2 be submodules of analytic Hilbert module X on Ω(C~n)such that M_1 M_2and dim M_1/M_2=k<∞.lf M_2 is an AF-cosubmodule,then the codimension dim M_1/M_2 ofM_2 in M_1 equals the cardinality of zeros of M_2 related to M_1 by counting multiplicities.Thecodimension formula has some interesting applications.In particular,the author calculates outthe dimension of Rudin quotient module,which is raised in 14].
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| 关 键 词： | 余维数公式 AF－余子模 解析Hilbert模 特征空间 Rudin商模 |
| 收稿时间： | 9/5/2000 12:00:00 AM |
THE CODIMENSION FORMULA ON AF-COSUBMODULES |
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| GUO Kunyu.THE CODIMENSION FORMULA ON AF-COSUBMODULES[J].Chinese Annals of Mathematics,Series B,2002,23(3):419-424. |
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| Authors: | GUO Kunyu |
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| Institution: | Department of Mathematics,Fudan University,Shanghai 200433,China. |
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| Abstract: | Let M1, M2 be submodules of analytic Hilbert module X on ?(? Cn) such that M1 ? M2 and dimM1/M2 = k < ". If M2 is an AF-cosubmodule, then the codimension dimM1/M2 of M2 in M1 equals the cardinality of zeros of M2 related to MI by counting multiplicities. The codimension formula has some interesting applications. In particular, the author calculates out the dimension of Rudin quotient module, which is raised in 14]. |
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| Keywords: | AF-cosubmodule Characteristic space Analytic Hilbert module |
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