10 citations · 17 across the 23 of their papers we have counts for
24 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…
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…
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.…
On, Around, and Beyond Frobenius' Theorem on Division Algebras
Matej Brešar, Victor S. Shulman
Frobenius' Theorem states that the algebra of quaternions is, besides the fields of real and complex numbers, the only finite-dimensional real division algebra. We firs…