Operator Frames for Banach Spaces

被引：5
|
作者：
Li, Chun-Yan [1 ]
机构：
[1] Chongqing Univ Sci & Technol, Dept Math & Phys, Chongqing 401331, Peoples R China
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2012年 / 6卷 / 01期
关键词：
Operator Bessel sequence; Operator frame; Operator Riesz basis; Banach space; P-FRAMES; SUBSPACES; DECOMPOSITIONS;
D O I：
10.1007/s11785-010-0076-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and operator Riesz bases are characterized by the analysis operator of operator Bessel sequences.
引用
收藏
页码：1 / 21
页数：21
相关论文
共 50 条
  • [41] AN OPERATOR SUMMABILITY OF SEQUENCESIN BANACH SPACES
    Karn, Anil Kumar
    Sinha, Deba Prasad
    GLASGOW MATHEMATICAL JOURNAL, 2014, 56 (02) : 427 - 437
  • [42] SINGULAR OPERATOR IN SCALE OF BANACH SPACES
    OVSYANNI.LV
    DOKLADY AKADEMII NAUK SSSR, 1965, 163 (04): : 819 - &
  • [43] On Ergodic Operator Means in Banach Spaces
    Alexandru Aleman
    Laurian Suciu
    Integral Equations and Operator Theory, 2016, 85 : 259 - 287
  • [44] Incomparable Banach spaces and operator semigroups
    Aiena, P
    González, M
    Martínez-Abejón, A
    ARCHIV DER MATHEMATIK, 2002, 79 (05) : 372 - 378
  • [45] Operator Space Structures on Banach Spaces
    Kumar, Vinod P.
    Balasubramani, M. S.
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2016, 40 (04) : 593 - 602
  • [46] FRAMES AND RIESZ BASES FOR BANACH SPACES, AND BANACH SPACES OF VECTOR-VALUED SEQUENCES
    Cho, Kyugeun
    Kim, Ju Myung
    Lee, Han Ju
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2013, 7 (02): : 172 - 193
  • [47] REFLEXIVE OPERATOR ALGEBRAS ON BANACH SPACES
    Merlevede, Florence
    Peligrad, Costel
    Peligrad, Magda
    PACIFIC JOURNAL OF MATHEMATICS, 2014, 267 (02) : 451 - 464
  • [48] On Ergodic Operator Means in Banach Spaces
    Aleman, Alexandru
    Suciu, Laurian
    INTEGRAL EQUATIONS AND OPERATOR THEORY, 2016, 85 (02) : 259 - 287
  • [49] Operator Lipschitz functions on Banach spaces
    Rozendaal, Jan
    Sukochev, Fedor
    Tomskova, Anna
    STUDIA MATHEMATICA, 2016, 232 (01) : 57 - 92
  • [50] Incomparable Banach spaces and operator semigroups
    P. Aiena
    M. González
    A. Martínez-Abejón
    Archiv der Mathematik, 2002, 79 : 372 - 378
12345