K-Frames from Finite Extensions

被引：3
作者：
Rahmani, Morteza [1 ]
机构：
[1] Islamic Azad Univ, Ilkhchi Branch, Young Researchers & Elite Club, Ilkhchi, Iran
来源：
RESULTS IN MATHEMATICS | 2022年 / 77卷 / 03期
关键词：
Bessel sequence; frame; K-frame;
D O I：
10.1007/s00025-022-01639-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study finite extensions of Bessel sequences to K-frames in a separable Hilbert space H. Precisely, we give some necessary and sufficient conditions for a Bessel sequence such that it can be expanded to a K-frame and a Parseval K-frame by adding finite number of elements in H. Also we show that under some conditions, a frame can be extended to a Parseval K-frame.
引用
收藏
页数：13
相关论文
共 15 条
  • [1] Arveson WB., 2002, SHORT COURSE SPECTRA, DOI [10.1007/b97227, DOI 10.1007/B97227]
  • [2] FINITE EXTENSIONS OF BESSEL SEQUENCES
    Bakic, Damir
    Beric, Tomislav
    [J]. BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2015, 9 (04): : 1 - 13
  • [3] Casazza PG, 2008, CONTEMP MATH, V451, P11
  • [4] Christensen O., 2008, FRAMES BASES INTRO C, DOI DOI 10.1007/978-0-8176-4678-3
  • [5] Extensions of Bessel sequences to dual pairs of frames
    Christensen, Ole
    Kim, Hong Oh
    Kim, Rae Young
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2013, 34 (02) : 224 - 233
  • [6] Weaving K-Frames in Hilbert Spaces
    Deepshikha
    Vashisht, Lalit K.
    [J]. RESULTS IN MATHEMATICS, 2018, 73 (02)
  • [7] Douglas R.G., 1998, GRADUATE TEXTS MATH, V179
  • [8] Frames for operators
    Gavruta, Laura
    [J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2012, 32 (01) : 139 - 144
  • [9] Some Results About the Operator Perturbation of a K-Frame
    Jia, Man
    Zhu, Yu-Can
    [J]. RESULTS IN MATHEMATICS, 2018, 73 (04)
  • [10] Expansion of frames to tight frames
    Li, Deng Feng
    Sun, Wen Chang
    [J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2009, 25 (02) : 287 - 292
12