2015/09/23 by Monojit Bhattacharjee, Bhattacharjee, M., Jörg Eschmeier +5 · 2 citations
Mathematics · #30H05 #46E22 #46M05 #46N99 #47A13 #47A15 #47A20 #47A45 #47B32 #47B38 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1509.07084
openalex publication_date 2015/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces HK on the unit ball in \mathbb Cn, wandering subspaces for restrictions of the multiplication tuple Mz = (Mz1, … ,Mzn) can be described in terms of suitable HK-inner functions. We prove that HK-inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogenous polynomials as an application. Along the way we prove a refinement of a result of Arveson on the uniqueness of minimal dilations of pure row contractions.