Dimension and universality on frames

被引：9
作者：
Iliadis, S. D. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Gen Topol & Geometry, Moscow 119991, Russia
来源：
TOPOLOGY AND ITS APPLICATIONS | 2016年 / 201卷
关键词：
Lattice; Frame; Dimension on frames; Universal frame; Saturated class of frames; Decomposition invariant; SPACES;
D O I：
10.1016/j.topol.2015.12.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we first introduce the notion of a saturated class of frames and then define a dimension-like invariant of a frame, the so-called decomposition invariant denoted by dec, which is a cardinal (in particular maybe a non-negative integer), and using the notion of the saturated class prove that in the class of all frames of weight less than or equal to a fixed infinite cardinal tau having decomposition invariant <= mu, where mu is a fixed cardinal less than or equal to tau, there are universal elements. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：92 / 109
页数：18
相关论文
共 50 条
  • [31] New characterizations of fusion frames (frames of subspaces)
    Asgari, Mohammad Sadegh
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2009, 119 (03): : 369 - 382
  • [32] SOME RESULTS ON FRAMES AND G-FRAMES
    Sadri, Vahid
    Ahmadi, Reza
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2018, 80 (04): : 99 - 108
  • [33] Frames and outer frames for Hilbert C*-modules
    Arambasic, Lj.
    Bakic, D.
    LINEAR & MULTILINEAR ALGEBRA, 2017, 65 (02) : 381 - 431
  • [34] Some algebraic characterizations of F-frames
    Dube, Themba
    ALGEBRA UNIVERSALIS, 2009, 62 (2-3) : 273 - 288
  • [35] FRAMES, SEMI-FRAMES, AND HILBERT SCALES
    Antoine, J. -P.
    Balazs, P.
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2012, 33 (7-9) : 736 - 769
  • [36] Coverages Give Free Constructions for Partial Frames
    Frith, John
    Schauerte, Anneliese
    APPLIED CATEGORICAL STRUCTURES, 2017, 25 (03) : 303 - 321
  • [37] Optimal dual frames for uniform frames with erasures
    Shuai, Fang
    Leng, Jingsong
    Gao, Qing
    Li, Jianbo
    2015 12TH INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS AND KNOWLEDGE DISCOVERY (FSKD), 2015, : 920 - 924
  • [38] New characterizations of fusion frames (frames of subspaces)
    Mohammad Sadegh Asgari
    Proceedings - Mathematical Sciences, 2009, 119 : 369 - 382
  • [39] Coverages Give Free Constructions for Partial Frames
    John Frith
    Anneliese Schauerte
    Applied Categorical Structures, 2017, 25 : 303 - 321
  • [40] Weaving g-Frames and Weaving Fusion Frames
    Amir Khosravi
    Jamaleh Sohrabi Banyarani
    Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42 : 3111 - 3129
12345