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8 papers · 1 filter
Greedy bases for Besov spaces
S. J. Dilworth, D. Freeman, E. Odell +1
We prove thatthe Banach space , which is isomorphic to certain Besov spaces, has a greedy basis whenever and $1<q<\inf…
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…
A new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces
G. Androulakis, S. J. Dilworth, N. J. Kalton
We give a new approach to the Ramsey-type results of Gowers on block bases in Banach spaces and apply our results to prove the Gowers dichotomy in F-spaces.
Descriptive set theoretic methods applied to strictly singular and strictly cosingular operators
G. Androulakis, K. Beanland
The class of strictly singular operators originating from the dual of a separable Banach space is written as an increasing union of subclasses which are defined using the Sch…
Products and Factors of Banach function spaces
Anton R. Schep
Given two Banach function spaces we study the pointwise product space E.F, especially for the case that the pointwise product of their unit balls is again convex. We then give cond…
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…