Invariance Preserving Conjugations on the Hardy Space

Arup Chattopadhyay; Supratim Jana

Invariance Preserving Conjugations on the Hardy Space

Functional Analysis 2026-07-15 v1

Authors: Arup Chattopadhyay , Supratim Jana

Abstract

We obtain a complete characterization of the class of conjugation operators $C$ on $H^2$ that map shift-invariant subspaces to shift-invariant subspaces. Alongside, we also obtain the existence and non-existence of conjugations that send shift-invariant subspaces to coinvariant subspaces.

Keywords

Hardy space conjugation operators shift-invariant subspaces coinvariant subspaces characterization

Cite

@article{arxiv.2607.13915,
  title  = {Invariance Preserving Conjugations on the Hardy Space},
  author = {Arup Chattopadhyay and Supratim Jana},
  journal= {arXiv preprint arXiv:2607.13915},
  year   = {2026}
}

Comments

10 pages, comments are welcome