Helson-Lowdenslager and de Branges type theorems in the setting of continuous rotationally symmetric norms

2023/03/31 by Apoorva Singh, Singh, Apoorva, Niteesh Sahni +1
Mathematics · #47B38 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47A15 #Secondary 30H10 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2303.17994

openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28

Abstract

A Helson-Lowdenslager type result has been proved by Chen in the context of Lebesgue spaces of the unit circle equipped with a continuous rotationally symmetric norm by studying the simply invariant subspaces of the operator of multiplication by the coordinate function z. In this paper, we generalize Chen's result by obtaining a description of simply invariant subspaces for multiplication by zⁿ. A de Branges type result is also proved for Hardy spaces equipped with continuous rotationally symmetric norms.

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