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

2026/07/17 by 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 H belongs to the class Δ(H) defined in [56]. This gives an affirmative solution to the (hyper) invariant subspace problem in H. Our method of proof is based on Berezin symbol technique in reproducing kernel Hilbert spaces.

Citations

• On two problems concerning linear transformations in hilbert space

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