Abstract
It is proved that the commutative algebra A of operators on a reflexive real Banach space has an invariant subspace if each operator T ∈ A satisfies the condition
where ║ · ║ e denotes the essential norm. This implies the existence of an invariant subspace for any commutative family of essentially self-adjoint operators on a real Hilbert space.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 1, pp. 65–69, 2018
Original Russian Text Copyright © by V. I. Lomonosov and V. S. Shul’man
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Lomonosov, V.I., Shul’man, V.S. Invariant Subspaces for Commuting Operators on a Real Banach Space. Funct Anal Its Appl 52, 53–56 (2018). https://doi.org/10.1007/s10688-018-0207-6
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DOI: https://doi.org/10.1007/s10688-018-0207-6