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Proof of Audenaert-Kittaneh's Conjecture

Teng Zhang

Abstract

By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to $p$-Schatten classes. This generalizes the main result obtained by McCarthy in [Israel J. Math. 5 (1967)].

Proof of Audenaert-Kittaneh's Conjecture

Abstract

By using the Three-lines theorem for a certain analytic function defined in terms of the trace and a duality argument method, we prove Audenaert-Kittaneh's conjecture related to -Schatten classes. This generalizes the main result obtained by McCarthy in [Israel J. Math. 5 (1967)].
Paper Structure (3 sections, 9 theorems, 39 equations)

This paper contains 3 sections, 9 theorems, 39 equations.

Table of Contents

  1. Introduction
  2. Proof of Audenaert-Kittaneh's conjecture
  3. Further remarks

Key Result

Theorem 1.1

Let $A,B\in \mathbb{B}_p(\mathscr{H})$. Then for $0<p\le 2$, and for $p\ge 2$,

Theorems & Definitions (12)

  • Theorem 1.1: McCarthy
  • Theorem 1.2: Hirazallah & Kittaneh HK08
  • Theorem 1.3: Ball, Carlen & Lieb
  • Theorem 1.4: McCarthy
  • Theorem 1.5: Conde & Moslehian
  • Lemma 2.1: Three-lines theorem, see U08
  • Lemma 2.2
  • proof
  • Theorem 2.3
  • proof
  • ...and 2 more