Characterizing Riesz bases via biorthogonal Bessel sequences

被引：1
|
作者：
E., Zikkos [1 ]
机构：
[1] Khalifa Univ, Abu Dhabi, U Arab Emirates
来源：
CARPATHIAN MATHEMATICAL PUBLICATIONS | 2023年 / 15卷 / 02期
关键词：
Riesz-Fischer sequence; Bessel sequence; Riesz sequence; Riesz basis; biorthogonal sequence; completeness;
D O I：
10.15330/cmp.15.2.377-380
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently D.T. Stoeva proved that if two Bessel sequences in a separable Hilbert space H are biorthogonal and one of them is complete in H, then both sequences are Riesz bases for 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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页码：377 / 380
页数：4
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