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.
引用
下载
收藏
页码：377 / 380
页数：4
相关论文
共 50 条
  • [21] CLASSIFICATION OF BIORTHOGONAL SEQUENCES
    RUCKLE, WH
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1974, 26 (03): : 721 - 733
  • [22] CLASSIFICATION OF BIORTHOGONAL SEQUENCES
    RUCKLE, WH
    NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (05): : A648 - &
  • [23] Modular Riesz bases versus Riesz bases in Hilbert C*-modules
    Hasannasab, Marzieh
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2021, 14 (01)
  • [24] On biorthogonal discrete wavelet bases
    Farkov, Yu. A.
    Rodionov, E. A.
    INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 2015, 13 (01)
  • [25] Riesz multiwavelet bases
    Han, B
    Kwon, SG
    Park, SS
    APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2006, 20 (02) : 161 - 183
  • [26] STABILITY OF RIESZ BASES
    Marchenko, Vitalii
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146 (08) : 3345 - 3351
  • [27] Spline wavelets and biorthogonal bases
    Proceedings of the Summer School in Numerical Analysis, 1992, 2
  • [28] Riesz bases by replacement
    De Carli, Laura
    Edward, Julian
    SAMPLING THEORY SIGNAL PROCESSING AND DATA ANALYSIS, 2022, 20 (02):
  • [29] Combining Riesz bases
    Gady Kozma
    Shahaf Nitzan
    Inventiones mathematicae, 2015, 199 : 267 - 285
  • [30] Combining Riesz bases
    Kozma, Gady
    Nitzan, Shahaf
    INVENTIONES MATHEMATICAE, 2015, 199 (01) : 267 - 285
12345