DECOMPOSITIONS OF COMPLETELY BOUNDED MAPS INTO COMPLETELY POSITIVE MAPS INVOLVING TRACE CLASS OPERATORS

被引：0
|
作者：
Li, Yuan [1 ]
Cui, Mengqian [1 ]
Wu, Jiao [1 ]
机构：
[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China
来源：
ANNALS OF FUNCTIONAL ANALYSIS | 2019年 / 10卷 / 01期
基金：
美国国家科学基金会;
关键词：
completely positive maps; completely bounded maps; trace class operators; EXTENSION;
D O I：
10.1215/20088752-2018-0005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let K(H) and B(H) be the sets of all compact operators and all bounded linear operators, respectively, on the Hilbert space H. In this article, we mainly show that if Phi is an element of CB(K(H)*, B(K)), then there exist Phi(i) is an element of CP(K(H)*, B(K)), for i = 1, 2, 3, 4, such that Phi = (Phi(1) - Phi(2)) + root-1(Phi(3)-Phi(4)). However, CP(K(H)*, B(K)) not subset of CB(K(H)*, B(K)), where CB(V, W) and CP(V, W) are the sets of all completely bounded maps and all completely positive maps from V into W, respectively.
引用
收藏
页码：16 / 28
页数：13
相关论文
共 50 条
  • [21] REGULAR REPRESENTATIONS OF COMPLETELY BOUNDED MAPS
    Bhat, B. V. Rajarama
    Mallick, Nirupama
    Sumesh, K.
    [J]. PACIFIC JOURNAL OF MATHEMATICS, 2017, 289 (02) : 257 - 286
  • [22] COMMUTANT REPRESENTATIONS OF COMPLETELY BOUNDED MAPS
    PAULSEN, VI
    SUEN, CY
    [J]. JOURNAL OF OPERATOR THEORY, 1985, 13 (01) : 87 - 101
  • [23] DILATIONS OF COMPLETELY POSITIVE MAPS
    DAVIES, EB
    [J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1978, 17 (APR): : 330 - 338
  • [24] THE PURIFICATION OF COMPLETELY POSITIVE MAPS
    DEMOEN, B
    [J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1982, 14 (NOV) : 545 - 548
  • [25] Gruss inequality for completely bounded maps
    Peric, I
    Rajic, R
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 390 : 287 - 292
  • [26] Completely bounded maps and invariant subspaces
    M. Alaghmandan
    I. G. Todorov
    L. Turowska
    [J]. Mathematische Zeitschrift, 2020, 294 : 471 - 489
  • [27] Roots of completely positive maps
    Bhat, B. V. Rajarama
    Hillier, Robin
    Mallick, Nirupama
    Kumar, Vijaya U.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 587 : 143 - 165
  • [28] Nilpotent completely positive maps
    Bhat, B. V. Rajarama
    Mallick, Nirupama
    [J]. POSITIVITY, 2014, 18 (03) : 567 - 577
  • [29] PERSPECTIVES AND COMPLETELY POSITIVE MAPS
    Hansen, Frank
    [J]. ANNALS OF FUNCTIONAL ANALYSIS, 2017, 8 (02): : 168 - 176
  • [30] Covariant completely positive maps
    Xu, TZ
    [J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2003, 34 (08): : 1131 - 1140
12345