Pavlos Motakis

A reflexive hereditarily indecomposable space with the hereditary invariant subspace property

A reflexive hereditarily indecomposable Banach space XISP is presented, such that for every Y infinite dimensional closed subspace of XISP and every bounded linear operator T : Y ! Y , the operator T admits a non-trivial closed invariant subspace.

A dual method of constructing hereditarily indecomposable Banach spaces

A new method of defining hereditarily indecomposable Banach spaces is presented. This method provides a unified approach for constructing reflexive HI spaces and also HI spaces with no reflexive subspace. All the spaces presented here satisfy the property that the composition of any two strictly singular operators is a compact one. This yields the first known example of a Banach space with no reflexive subspace such that every operator has a non-trivial closed invariant subspace.

ON THE STRUCTURE OF SEPARABLE -SPACES

Based on a construction method introduced by J. Bourgain and F. Delbaen, we give a general definition of a Bourgain-Delbaen space and prove that every infinite dimensional separable

Examples of

\mathcal{L}_\infty

k

-space is isomorphic to such a space. Furthermore, we provide an example of a

-iterated spreading models

\mathcal{L}_\infty

A metric interpretation of reflexivity for Banach spaces

and asymptotic

THE STABILIZED SET OF p'S IN KRIVINE'S THEOREM CAN BE DISCONNECTED

c_0

Strictly singular operators in Tsirelson like spaces

space not containing

Arbitrarily distortable Banach spaces of higher order

c_0