10 citations · 17 across the 23 of their papers we have counts for
19 papers · 1 filter
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…
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…
Pontryagin-Krein Theorem: Lomonosov's proof and related results
Edward Kissin, Victor S. Shulman, Yurii Turovskii
We discuss Lomonosov's proof of the Pontryagin-Krein Theorem on invariant maximal non-positive subspaces, prove the refinement of one theorem from \cite{OShT} on common fixed point…
From Lomonosov Lemma to Radical Approach in Joint Spectral Radius Theory
Edward Kissin, Victor S. Shulman, Yurii Turovskii
In this paper we discuss the infinite-dimensional generalizations of the famous theorem of Berger-Wang (generalized Berger-Wang formulas) and give an operator-theoretic proof of I.…
Relations and radicals in abstract lattices and in lattices of subspaces of Banach spaces and ideals of Banach algebras. Amitsur's theory revisited
Edward Kissin, Victor S. Shulman, Yuri Turovskii
We refine Amitsur's theory of radicals in complete lattices and apply the obtained results to the theory of radicals in the lattices of subspaces of Banach spaces and in the lattic…
Reduced spectral synthesis and compact operator synthesis
V. S. Shulman, I. G. Todorov, L. Turowska
We introduce and study the notion of reduced spectral synthesis, which unifies the concepts of spectral synthesis and uniqueness in locally compact groups. We exhibit a number of e…