Some new equivalences of Anderson's paving conjectures

2007/06/18 by Vern I. Paulsen, Paulsen, Vern I., Mrinal Raghupathi +1
Mathematics · #46L15 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L15

paper · pdf · doi:10.48550/arxiv.0706.2644

Typos corrected, references added

openalex publication_date 2007/06/18 · arxiv created 2007/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Anderson's paving conjectures are known to be equivalent to the Kadison-Singer problem. We prove some new equivalences of Anderson's conjectures that require the paving of smaller sets of matrices. We prove that if the strictly upper triangular operatorss are pavable, then every 0 diagonal operator is pavable. This result follows from a new paving condition for positive operators. In addition, we prove that if the upper triangular Toeplitz operators are paveable, then all Toeplitz operators are paveable.

Related

• Projections and the Kadison-Singer Problem
• Asymptotically Optimal Multi-Paving
• The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections
• The paving conjecture is equivalent to the paving conjecture for triangular matrices
• A counterexample to a conjecture of Akemann and Anderson