Cyclicity of the shift operator and a related completeness problem in de Branges-Rovnyak spaces

2024/03/07 by Fricain, Emmanuel, Lebreton, Romain
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2403.04335

Abstract

In this paper, we study the cyclic vectors of the shift operator S_b acting on de Branges-Rovnyak space \mathcal H(b) associated to a non-extreme point of the closed unit ball of H^∞. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity.

Related

• Cyclicity in de Branges--Rovnyak spaces
• Cyclicity of the shift operator through Bezout identities
• Completely hyperexpansive operators with finite rank defect operator and de Branges-Rovnyak spaces
• The Cowen-Douglas class and de Branges-Rovnyak spaces
• Reducing Subspaces of de Branges-Rovnyak Spaces