It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequence. Here we prove that the completeness of one (any one) of the biorthogonal sequences can be removed from the characterization.

中文翻译：

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关于通过双正交序列表征Riesz碱基

众所周知，希尔伯特空间中的序列当且仅当是具有双正交序列的完整贝塞尔序列且也是完整贝塞尔序列时才是Riesz基。在这里，我们证明了一个（任意一个）生物正交序列的完整性可以从表征中去除。