most citedAlmost invariant half-spaces of algebras of operators

2 citations · 2 across the 3 of their papers we have counts for

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3 papers

math.FA2009★ 2 cited

Almost invariant half-spaces of algebras of operators

Alexey I. Popov

Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY is a subspace of Y+F for some finite-dimensional ``error'' F. In th…

math.FA2009

Almost invariant half-spaces of operators on Banach spaces

George Androulakis, Alexey I. Popov, Adi Tcaciuc +1

We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banach space has an almost invariant half-space, that is, a s…

math.FA2008

A version of Lomonosov's theorem for collections of positive operators

Alexey I. Popov, Vladimir G. Troitsky

It is known that for every Banach space X and every proper WOT-closed subalgebra A of L(X), if A contains a compact operator then it is not transitive. That is, there exist non-zer…