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Constructing $k$-Kadison-Schwarz maps

Farrukh Mukhamedov, Dariusz Chruściński

Abstract

We study k Kadison Schwarz (k KS) mappings on matrix algebras and derive explicit conditions ensuring the k KS property for two classes of maps parameterized by a single k-positive map.

Constructing $k$-Kadison-Schwarz maps

Abstract

We study k Kadison Schwarz (k KS) mappings on matrix algebras and derive explicit conditions ensuring the k KS property for two classes of maps parameterized by a single k-positive map.
Paper Structure (8 sections, 11 theorems, 97 equations)

This paper contains 8 sections, 11 theorems, 97 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Class of $k$-Kadison-Schwarz operators
  4. Generalized Reduction Maps
  5. Generalized Depolarized Maps
  6. KS-decomposability
  7. Proof of Theorem \ref{['HS']}
  8. Proof of Theorem \ref{['dKS1']}

Key Result

Theorem 2.3

MA2010 The following assertions hold true:

Theorems & Definitions (24)

  • Definition 2.1
  • Remark 2.2
  • Theorem 2.3
  • Definition 2.4
  • Definition 2.5
  • Theorem 2.6
  • Lemma 2.7
  • Proposition 2.8
  • proof
  • Remark 2.9
  • ...and 14 more