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A weak Hilbert space that is a twisted HIlbert space

Jesús Suárez

TL;DR

The paper constructs a weak Hilbert space that is a twisted Hilbert space by defining $Z(T^2)=d(T^2,(T^2)^*)_{1/2}$ via complex interpolation between $T^2$ and its dual. It proves that $Z(T^2)$ is a twisted Hilbert space that is not isomorphic to a Hilbert space, nor to subspaces or quotients of known Kalton–Peck or Enflo–Lindenstrauss–Pisier constructions such as $Z_2(\

Abstract

We construct a weak Hilbert space that is a twisted Hilbert space.

A weak Hilbert space that is a twisted HIlbert space

TL;DR

The paper constructs a weak Hilbert space that is a twisted Hilbert space by defining via complex interpolation between and its dual. It proves that is a twisted Hilbert space that is not isomorphic to a Hilbert space, nor to subspaces or quotients of known Kalton–Peck or Enflo–Lindenstrauss–Pisier constructions such as $Z_2(\

Abstract

We construct a weak Hilbert space that is a twisted Hilbert space.
Paper Structure (2 sections, 10 theorems, 43 equations)

This paper contains 2 sections, 10 theorems, 43 equations.

Table of Contents

  1. Introduction
  2. The example

Key Result

Proposition 1

The space $dX_{\theta}$ and $d_{\Omega_{\rho}}X_{\theta}$ coincide, with equivalent quasi-norms.

Theorems & Definitions (19)

  • Definition 1
  • Proposition 1
  • Proposition 2
  • Lemma 1
  • proof
  • Proposition 3
  • proof
  • Theorem 1
  • proof
  • Proposition 4
  • ...and 9 more