Projective positivity of the function systems

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DOSİ A.

Positivity, vol.27, no.4, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1007/s11117-023-00997-3
  • Journal Name: Positivity
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Business Source Elite, Business Source Premier, MathSciNet, zbMATH
  • Keywords: Function system, Operator system, Projective positivity, State space, Unital cone
  • Middle East Technical University Affiliated: Yes

Abstract

The present paper is devoted to the projective positivity in the category of function systems, which plays a key role in the quantization problems of the operator systems. The main result of the paper asserts that every unital ∗ -normed space can be equipped with the projective positivity. The geometry of the related state spaces is described in the case of Lp -spaces, Schatten matrix spaces, and Lp -spaces of a finite von Neumann algebra.