On the solution of Kim, Pearcy and Shields problem and its consequences

Mubariz T. Garayev

On the solution of Kim, Pearcy and Shields problem and its consequences

Functional Analysis 2026-07-17 v1

Authors: Mubariz T. Garayev

Abstract

We give a negative answer to a question due to Kim, Pearcy and Shields, namely, we prove that every nonscalar bounded linear operator on a Hilberts space $\mathcal{H}$ belongs to the class $\Delta(\mathcal{H})$ defined in [56]. This gives an affirmative solution to the (hyper) invariant subspace problem in $\mathcal{H}$ . Our method of proof is based on Berezin symbol technique in reproducing kernel Hilbert spaces.

Keywords

invariant subspace problem Berezin symbol reproducing kernel Hilbert space bounded linear operator nonscalar operator

Cite

@article{arxiv.2607.16373,
  title  = {On the solution of Kim, Pearcy and Shields problem and its consequences},
  author = {Mubariz T. Garayev},
  journal= {arXiv preprint arXiv:2607.16373},
  year   = {2026}
}

Comments

19 pages, 89 references