Hölder inequality for symmetric operator spaces and trace property of K-cycles

2016/05/17 by Fedor Sukochev, F. Sukochev
Mathematics · #Advanced Operator Algebra Research #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory

paper · doi:10.1112/blms/bdw022

Abstract

We prove a general version of the Hölder inequality for symmetric operator spaces and symmetric functionals (traces) on such spaces, answering some open questions in the literature. We also prove a general version of the result establishing the trace property of the non-commutative integral defined via an arbitrary positive symmetric functional on a symmetric operator space. Our main tool is the so-called uniform Hardy–Littlewood majorization.

Related

• Holder's inequality for roots of symmetric operator spaces
• Symmetric functionals on simply generated symmetric spaces
• Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals
• Traces on symmetrically normed operator ideals
• On the stabilization of relative trace formulae: descent and the\n fundamental lemma