Farrukh Mukhamedov, Hasan Akın, “Characterization of Bistochastic Kadison–Schwarz Operators on <nobr>$M_2(\mathbb C)$</nobr>”, Trudy Mat. Inst. Steklova, 2021, Volume 313,Pages <nobr>178

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Characterization of Bistochastic Kadison–Schwarz Operators on $M_2(\mathbb C)$

Farrukh Mukhamedov^a, Hasan Akın^b

^a Department of Mathematical Sciences, College of Science, United Arab Emirates University, 15551 Al Ain, United Arab Emirates
^b Gökkuşağı Mahallesi, 1164. Cd. No: 9, 06450 Çankaya, Ankara, Turkey

Abstract: We characterize bistochastic Kadison–Schwarz operators acting on $M_2(\mathbb C)$. The obtained characterization allows us to find positive operators that are not Kadison–Schwarz ones. Moreover, we provide several examples of Kadison–Schwarz operators which are not completely positive.

Keywords: bistochastic mapping, Kadison–Schwarz operator, complete positivity.

UDC: 517.98

Received: May 16, 2020
Revised: October 5, 2020
Accepted: February 15, 2021

DOI: 10.4213/tm4179