2018/12/16 by Ying‐Fen Lin, Ivan G. Todorov, Lin, Ying-Fen +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1812.06483
openalex publication_date 2018/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given C*-algebra A, we establish the existence of maximal and minimal operator A-system structures on an AOU A-space. In the case A is a W*-algebra, we provide an abstract characterisation of dual operator A-systems, and study the maximal and minimal dual operator A-system structures on a dual AOU A-space. We introduce operator-valued Schur multipliers, and provide a Grothendieck-type characterisation. We study the positive extension problem for a partially defined operator-valued Schur multiplier φ and, under some richness conditions, characterise its affirmative solution in terms of the equality between the canonical and the maximal dual operator A-system structures on an operator system naturally associated with the domain of φ.