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math.FA2022
On transitive operator algebras in real Banach spaces
Edward Kissin, Victor S. Shulman, Yurii V. Turovskii
We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally div…
math.FA2022
Some remarks on invariant subspaces in real Banach spaces (revised version)
V. I. Lomonosov, V. S. Shulman
It is proved that a commutative algebra of operators on a reflexive real Banach space has an invariant subspace if each operator satisfies the condition $$\|1- \vareps…