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February 2019 Decompositions of completely bounded maps into completely positive maps involving trace class operators
Yuan Li, Mengqian Cui, Jiao Wu
Ann. Funct. Anal. 10(1): 16-28 (February 2019). DOI: 10.1215/20088752-2018-0005

Abstract

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 ΦCB(K(H),B(K)), then there exist ΦiCP(K(H),B(K)), for i=1,2,3,4, such that Φ=(Φ1Φ2)+1(Φ3Φ4). However, CP(K(H),B(K))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.

Citation

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Yuan Li. Mengqian Cui. Jiao Wu. "Decompositions of completely bounded maps into completely positive maps involving trace class operators." Ann. Funct. Anal. 10 (1) 16 - 28, February 2019. https://doi.org/10.1215/20088752-2018-0005

Information

Received: 31 October 2017; Accepted: 9 February 2018; Published: February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07045482
MathSciNet: MR3899953
Digital Object Identifier: 10.1215/20088752-2018-0005

Subjects:
Primary: 47L25
Secondary: 46L07, 47L05

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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