Operator algebras with a reduction property

2013/11/15 by James A Gifford, Gifford, James A
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1311.3822

arxiv created 2013/11/15 · arxiv updated 2013/11/18

Abstract

In this thesis we explore the the possibility of characterising C* algebras by their (non-isometric) Banach algebra structure alone. We introduce a property of Banach algebras, the Total Reduction Property, and conjecture that a Banach algebra has this property if and only if it is isomorphic to a C* algebra. We establish some partial results in support of this conjecture.

Related

• Operator algebras: an informal overview
• Completely Bounded Characterization of Operator Algebras with Involution
• Isomorphisms of operator algebras
• The Lattice of C*-covers of an operator algebra
• Anti-C*-algebras