On characterizations of commutativity of C*-algebras

2003/03/25 by Guoxing Ji, Jun Tomiyama · 3 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.1090/s0002-9939-03-06991-0

Abstract

We give three kinds of characterizations of the commutativity of C <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="Superscript asterisk"> <mml:semantics> <mml:msup> <mml:mi/> <mml:mo> ∗ </mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">^*</mml:annotation> </mml:semantics> </mml:math> </inline-formula> - algebras. The first is the one from operator monotone property of functions regarded as the nonlinear version of Stinespring theorem, the second one is the characterization of commutativity of local type from expansion formulae of related functions and the third one is of global type from multiple positivity of those nonlinear positive maps induced from functions.

Cited by

• Differential analysis of matrix convex functions II
• Monotone operator functions on C^*-algebra
• A characterization of abelian C^*-algebras in terms of strong Birkhoff-James orthogonality

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