10 citations · 12 across the 13 of their papers we have counts for
13 papers
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…
Relation and radical approach to the theory of C*-algebras
Edward Kissin, Victor S. Shulman, Yurii V. Turovskii
In this paper we pursue three aims. The first one is to apply Amitsur's relations and radicals theory to the study of the lattices Id_{A} of closed two-sided ideals of C*-algebras…
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…
Topological radicals, V. From algebra to spectral theory
Victor S. Shulman, Yuri V. Turovskii
We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the sc…