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| THE CODIMENSION FORMULA ON AF-COSUBMODULES |
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Citation： |
GUO Kunyu.THE CODIMENSION FORMULA ON AF-COSUBMODULES[J].Chinese Annals of Mathematics B,2002,23(3):419~424 |
| Page view： 1107
Net amount： 753 |
Authors： |
GUO Kunyu; |
Foundation： |
Project supported by the National Natural Science Foundation of China (No. 10171019), and the Shuguan Project in Shanghai and the Young Teacher Fund of Higher School of the Ministry of Education of China. |
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| Abstract： |
Let $M_1,\,M_2$ be submodules of analytic Hilbert module $X$ on $\Omega(\subset C^n)$ such that $M_1\supseteq M_2$ and $\dim\, M_1/M_2=k<\infty.$ If $M_2$ is an AF-cosubmodule, then the codimension $\dim\,M_1/M_2$ of $M_2$ in $M_1$ equals the cardinality of zeros of $M_2$ related to $M_1$ 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]. |
Keywords： |
AF-cosubmodule, Characteristic space, Analytic Hilbert module |
Classification： |
46J15, 47A15 |
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