On characterizations of bistochastic Kadison-Schwarz operators on $M_2(\mathbb{C})$
Farrukh Mukhamedov, Hasan Akin
TL;DR
This paper characterizes bistochastic Kadison-Schwarz operators on 2x2 complex matrices, identifying positive but not Kadison-Schwarz operators and constructing Kadison-Schwarz operators that are not completely positive.
Contribution
It provides a detailed description of bistochastic Kadison-Schwarz operators on $M_2(C)$, including new examples of positive but non-Kadison-Schwarz and non-completely positive operators.
Findings
Identified positive operators that are not Kadison-Schwarz
Constructed Kadison-Schwarz operators that are not completely positive
Provided a characterization of bistochastic Kadison-Schwarz operators
Abstract
In this paper we describe bistochastic Kadison-Schawrz operators acting on . Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of that characterization we construct Kadison-Schawrz operators, which are not completely positive.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Advanced Banach Space Theory