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Finiteness of metrics on state spaces

David Kyed, Ryszard Nest

Abstract

We show that Connes' metric on the state space associated with a spectral triple is nowhere infinite exactly when it is globally bounded. Moreover, we produce a family of simple examples showing that this is not automatically the case.

Finiteness of metrics on state spaces

Abstract

We show that Connes' metric on the state space associated with a spectral triple is nowhere infinite exactly when it is globally bounded. Moreover, we produce a family of simple examples showing that this is not automatically the case.
Paper Structure (2 sections, 24 equations)

This paper contains 2 sections, 24 equations.

Table of Contents

  1. Introduction
  2. Proofs

Theorems & Definitions (4)

  • proof : Proof of Theorem \ref{['thm:main-thm-A']}
  • Remark 2.1
  • Remark 2.2
  • proof : Proof of Theorem \ref{['thm:main-thm-B']}