Research Article
Fixed points of completely positive maps and its dual maps *
https://doi.org/10.21203/rs.3.rs-2233069/v1
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published 27 Dec, 2022
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Let A ⊂ B(H) be a row contraction and Φ_A determined by A be a completely positive map on B(H). In this paper, we mainly consider fixed points of Φ_A and its dual map {Φ_A}^ † . It is given that Φ_A(X) ≤ X (or Φ_A(X) ≥ X) implies Φ_A(X) = X and {Φ_A}^ † (X) = X when X ∈ B(H) is a compact operator. Some necessary conditions of Φ_A(X) = X and {Φ_A}^ † (X) = X are given.
MR (2010) Subject Classification 47A05; 47A62
Quantum operation
dual operation
fixed point
compact operator.
No competing interests reported.
published 27 Dec, 2022
Read the published version in Journal of Inequalities and Applications →
Editorial decision: Major revision
21 Nov, 2022
Reviews received at journal
19 Nov, 2022
Reviewers agreed at journal
07 Nov, 2022
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07 Nov, 2022
Editor assigned by journal
06 Nov, 2022
Submission checks completed at journal
06 Nov, 2022
First submitted to journal
03 Nov, 2022
You are reading this latest preprint version