5 papers
Almost-invariant and essentially-invariant halfspaces
Gleb Sirotkin, Ben Wallis
In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if is an infinite-dimensional complex Banach…
Sequence-singular operators
Gleb Sirotkin, Ben Wallis
In this paper we study two types of collections of operators on a Banach space on the subject of forming operator ideals. One of the types allows us to construct an uncountable cha…
Classes of strictly singular operators and their products
George Androulakis, Pandelis Dodos, Gleb Sirotkin +1
V. D. Milman proved in \cite{Milman:70} that the product of two strictly singular operators on () or on is compact. In this note we utilize Schre…
Narrow operators on vector-valued sup-normed spaces
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy +2
We characterise narrow and strong Daugavet operators on -spaces; these are in a way the largest sensible classes of operators for which the norm equation $\|Id+T\| = 1+\|T\…
Banach spaces with the Daugavet property
Vladimir Kadets, Roman Shvidkoy, Gleb Sirotkin +1
A Banach space is said to have the Daugavet property if every operator of rank~ satisfies . We show that then every weakly compact operator s…