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Winter 2018 Positive map as difference of two completely positive or super-positive maps
Tsuyoshi Ando
Adv. Oper. Theory 3(1): 53-60 (Winter 2018). DOI: 10.22034/aot.1702-1129

Abstract

For a linear map from ${\mathbb M}_m$ to ${\mathbb M}_n$, besides the usual positivity, there are two stronger notions, complete positivity and super positivity. Given a positive linear map $\varphi$ we study a decomposition $\varphi = \varphi^{(1)} - \varphi^{(2)}$ with completely positive linear maps $\varphi^{(j)} (j = 1,2)$. Here $\varphi^{(1)} + \varphi^{(2)}$ is of simple form with norm small as possible. The same problem is discussed with super-positivity in place of complete positivity.

Citation

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Tsuyoshi Ando. "Positive map as difference of two completely positive or super-positive maps." Adv. Oper. Theory 3 (1) 53 - 60, Winter 2018. https://doi.org/10.22034/aot.1702-1129

Information

Received: 25 February 2017; Accepted: 11 March 2017; Published: Winter 2018
First available in Project Euclid: 5 December 2017

zbMATH: 06804316
MathSciNet: MR3730339
Digital Object Identifier: 10.22034/aot.1702-1129

Subjects:
Primary: 47C15
Secondary: 15A69, 47A30

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 1 • Winter 2018
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