Dilations, wandering subspaces, and inner functions
Linear Algebra and Its Applications
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 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-homogeneous 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.
Bhattacharjee, M.; Eschmeier, J.; Keshari, Dinesh K.; and Sarkar, Jaydeb, "Dilations, wandering subspaces, and inner functions" (2017). Journal Articles. 2520.