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\(\left\{ {{e_n}} \right\}_{n = 1}^\infty \)是Hilbert空间H的规范正交基,A是H中的有界线性算子,设\[M_n={\left\{ {{e_1},{e_2}, \cdots ,{e_n}} \right\}^ \bot }\],如果\(\mathop {\sup }\limits_{x \in {M_n},\left\| x \right\| = 1} \left\| {Ax} \right\| \to 0(n \to \infty )\)
证明A是一个紧算子 |
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