2007/07/20 by Ronald G. Douglas, Jaydeb Sarkar, Douglas, Ronald G. +1 · 1 citation
Mathematics · #46E22 #46M20 #47A13 #47A20 #47A53 #47B32 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0707.3122
openalex publication_date 2007/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hardy space on the unit ball in Cn provides examples of a quasi-free, finite rank Hilbert module which contains a pure submodule isometrically isomorphic to the module itself. For n=1 the submodule has finite codimension. In this note we show that this phenomenon can only occur for modules over domains in the complex plain and for finitely-connected domains only for Hardy-like spaces, the bundle shifts. Moreover, we show for essentially reductive modules that even when the codimension is infinite, the module is subnormal and again, on nice domains such as the unit ball, must be Hardy-like.