Factorization of operator valued Lp for 0≤p<1

被引：0
|
作者：
Mezrag, L [1 ]
机构：
[1] Msila Univ, Dept Math, Ichbilia 28105, Msila, Algeria
来源：
MATHEMATISCHE NACHRICHTEN | 2004年 / 266卷
关键词：
convex operator; factorization; Kasin cotype; random variable;
D O I：
10.1002/mana.200310144
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In [5], it is proved that a bounded linear operator u, from a Banach space Y into an L,(S, v) factors through L-p1 (S, nu) for some p(1) > 1, if Y* is of finite cotype; (S, nu) is a probability space for p = 0, and any measure space for 0 < p < 1. In this paper, we generalize this result to uupsilon, where u : Y --> L-p(S, nu) and upsilon : X --> Y are linear operators such that upsilon* is of finite Kasin cotype. This result gives also a new proof of Grothendieck's theorem. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
引用
收藏
页码：60 / 67
页数：8
相关论文
共 50 条
  • [41] The "Full Muntz Theorem" in Lp [0,1] for 0 &lt; p &lt; ∞
    Erdélyi, T
    Johnson, WB
    [J]. JOURNAL D ANALYSE MATHEMATIQUE, 2001, 84 (1): : 145 - 172
  • [42] TheFineSpectraoftheDifferenceOperator△OvertheSequenceSpacebvp,（1≤p&lt;∞）
    Ali MAKHMEDOV
    Feyzi BASAR
    [J]. Acta Mathematica Sinica(English Series)., 2007, 23 (10) - 1768
  • [43] Order convexity and concavity of Lorentz spaces Λp,w, 0 &lt;p&lt;∞
    Kaminska, A
    Maligranda, L
    [J]. STUDIA MATHEMATICA, 2004, 160 (03) : 267 - 286
  • [44] The complete separation of the two finer asymptotic lp structures for 1=p&lt; 8
    Argyros, Spiros A.
    Georgiou, Alexandros
    Manoussakis, Antonis
    Motakis, Pavlos
    [J]. FORUM OF MATHEMATICS SIGMA, 2022, 10
  • [45] Computing the proximity operator of the p norm with 0 &lt; p &lt; 1
    Chen, Feishe
    Shen, Lixin
    Suter, Bruce W.
    [J]. IET SIGNAL PROCESSING, 2016, 10 (05) : 557 - 565
  • [46] Alternating Proximal Algorithm for L1/TVp (0 &lt;p&lt; 1) Image Recovery
    Xiao, Jin
    Yuan, Xiao
    [J]. TENTH INTERNATIONAL CONFERENCE ON GRAPHICS AND IMAGE PROCESSING (ICGIP 2018), 2019, 11069
  • [47] On the rate of tangential convergence of functions from hardy spaces, 0&lt;p&lt;1
    Hare, KE
    Stokolos, AM
    [J]. P-HARMONIC EQUATION AND RECENT ADVANCES IN ANALYSIS, 2005, 370 : 119 - 132
  • [48] Density of systems of trigonometric polynomials in Lp, 0 &lt; p &lt; 1
    Klotz, L.
    Kuersten, K. -D.
    [J]. ANALYSIS MATHEMATICA, 2008, 34 (02) : 105 - 117
  • [49] On generalized K-functionals in Lp for 0 &lt; p &lt; 1
    Kolomoitsev, Yurii
    Lomako, Tetiana
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (03) : 1016 - 1030
  • [50] On equivalence of moduli of smoothness of splines in Lp, 0 &lt; p &lt; 1
    Kopotun, Kirill A.
    [J]. JOURNAL OF APPROXIMATION THEORY, 2006, 143 (01) : 36 - 43
12345