Backward shift invariant subspaces in reproducing kernel Hilbert spaces

• Emmanuel Fricain ^[1] ; Javad Mashreghi ^[2] ; Rishika Rupam ^[1]
  1. [1] Université de Lille (Francia)
  2. [2] Université Lava (Canadá)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 126, Nº 1, 2020, págs. 142-160
• Idioma: inglés
• DOI: 10.7146/math.scand.a-119120
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• Resumen

  • In this note, we describe the backward shift invariant subspaces for an abstract class of reproducing kernel Hilbert spaces. Our main result is inspired by a result of Sarason concerning de Branges-Rovnyak spaces (the non-extreme case). Furthermore, we give new applications in the context of the range space of co-analytic Toeplitz operators and sub-Bergman spaces.