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math.FA2026
Invariant subspaces for operators with spectrum containing the boundary of the numerical range
Vladimir Müller, Yuri Tomilov
We prove that a bounded Hilbert space operator has a nontrivial invariant subspace whenever its spectrum contains the topological boundary of its numerical range. We also give vari…
math.FA2026
On similarity to contraction semigroups and tensor products, II: Infinite tensor products
Jesus Oliva-Maza, Yuri Tomilov
We develop a framework for infinite tensor products of Hilbert spaces, operators, and semigroups tailored to questions of similarity to contraction semigroups. On the operator-theo…