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arXiv · 2607.16373

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

Mubariz T. Garayev
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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.

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Mubariz T. Garayev. 2026-07-17. On the solution of Kim, Pearcy and Shields problem and its consequences. https://arxiv.org/abs/2607.16373

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