We construct a Banach space that does not contain any infinite unconditional basic
sequence and investigate further properties of this space. For example, it has no subspace …

A hereditarily indecomposable 多∞-space that solves the scalar-plus-compact problem
Page 1 Acta Math., 206 (2011), 1–54 DOI: 10.1007/s11511-011-0058-y c© 2011 by Institut …

This book on Banach space theory focuses on what have been called three-space
problems. It contains a fairly complete description of ideas, methods, results and …

We prove that Hilbert space is distortable and, in fact, arbitrarily distortable. This means that
for all lambda> 1 there exists an equivalent norm|.| on l_2 such that for all infinite …

The analysis of the characteristics of walks on ordinals is a powerful new technique for
building mathematical structures, developed by the author over the last twenty years. This is …

For a certain class of algebras A we give a method for constructing Banach spaces X such
that every operator on X is close to an operator in A. This is used to produce spaces with a …

This book contains two sets of notes prepared for the Advanced Course on R-sey Methods
in Analysis given at the Centre de Recerca Matematica in January 2004, as part of its year …

An infinite‐dimensional Banach space X is constructed which is not isomorphic to X⊕ R.
Equivalently, X is not isomorphic to any of its closed subspaces of codimension one. This …

Banach spaces provide a framework for modern mathematical analysis, as they blend
classical analysis, geometry, topology and linearity. This makes Banach space theory a …

EXAMPLES OF ASYMPTOTIC l1 BANACH SPACES Introduction A Banach space (X, ·) is λ-distortable
(λ > 1) if there exists an eq Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL …