利用双正交贝塞尔序列表征Riesz碱基

IF 1 Q1 MATHEMATICS Carpathian Mathematical Publications Pub Date : 2023-09-10 DOI:10.15330/cmp.15.2.377-380

E. Zikkos

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引用次数: 0

摘要

最近，D.T. Stoeva证明了如果可分离Hilbert空间$\mathcal H$中的两个贝塞尔序列是双正交的，并且其中一个在$\mathcal H$中是完全的，那么这两个序列都是$\mathcal H$的Riesz基。这改进了一个众所周知的结果，即假设两个序列都是完备的。在这篇笔记中，我们基于Riesz-Fischer序列的概念，给出了对Stoeva结果的一个相当简短和基本的替代证明。

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Characterizing Riesz bases via biorthogonal Bessel sequences

Recently D.T. Stoeva proved that if two Bessel sequences in a separable Hilbert space $\mathcal H$ are biorthogonal and one of them is complete in $\mathcal H$, then both sequences are Riesz bases for $\mathcal H$. This improves a well known result where completeness is assumed on both sequences. In this note we present an alternative proof of Stoeva's result which is quite short and elementary, based on the notion of Riesz-Fischer sequences.

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