Characterization of Invariant subspaces in the polydisc

2017/10/26 by Amit Maji, Aneesh Mundayadan, Maji, Amit +5
Computer Science · Mathematics · #30H05 #30H10 #32A10 #32A70 #46E22 #47A13 #47A15 #47A80 #47B32 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Control Systems and Analysis #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.CV #math.FA #math.OA #msc:30H05 #msc:30H10 #msc:32A10 #msc:32A70 #msc:46E22 #msc:47A13 #msc:47A15 #msc:47A80 #msc:47B32

paper · pdf · doi:10.48550/arxiv.1710.09853

23 pages, revised

openalex publication_date 2017/10/26 · arxiv created 2017/11/09 · arxiv updated 2017/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a complete characterization of invariant subspaces for (M_z1, …, M_zn) on the Hardy space H²(\mathbbDⁿ) over the unit polydisc \mathbbDⁿ in ℂⁿ, n >1. In particular, this yields a complete set of unitary invariants for invariant subspaces for (M_z1, …, M_zn) on H²(\mathbbDⁿ), n > 1. As a consequence, we classify a large class of n-tuples, n > 1, of commuting isometries. All of our results hold for vector-valued Hardy spaces over \mathbbDⁿ, n > 1. Our invariant subspace theorem solves the well-known open problem on characterizations of invariant subspaces of the Hardy space over the unit polydisc.

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