Invariant subspaces for commuting operators in a real Banach space

2016/12/17 by Victor Lomonosov, Lomonosov, Victor, Victor S. Shulman +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1612.05821

openalex publication_date 2016/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is proved that a commutative algebra A of operators in a reflexive real Banach space has an invariant subspace if each operator T∈ A satisfies the condition ‖1- ε T²‖_e ≤ 1 + o(ε) when ε\searrow 0, where ‖⋅‖_e is the essential norm. This implies the existence of an invariant subspace for every commutative family of essentially selfadjoint operators in a real Hilbert space.

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