2018/04/16 by Sibaprasad Barik, Barik, Sibaprasad, B. Krishna Das +3
Mathematics · #14M99 #30H10 #46E20 #47A13 #47A20 #47A56 #47B38 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1804.05621
openalex publication_date 2018/04/16 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Motivated by Ball, Li, Timotin and Trent's Schur-Agler class version of\ncommutant lifting theorem, we introduce a class, denoted by\n\Pn(\H), of n-tuples of commuting contractions on a\nHilbert space \H. We always assume that n \≥ 3. The importance\nof this class of n-tuples stems from the fact that the von Neumann inequality\nor the existence of isometric dilation does not hold in general for n-tuples,\nn \≥ 3, of commuting contractions on Hilbert spaces (even in the level of\nfinite dimensional Hilbert spaces). Under some rank-finiteness assumptions, we\nprove that tuples in \Pn(\H) always admit explicit\nisometric dilations and satisfy a refined von Neumann inequality in terms of\nalgebraic varieties in the closure of the unit polydisc in \ℂn.\n