1. CJM 2010 (vol 62 pp. 595)
2. CJM 2007 (vol 59 pp. 63)
 Ferenczi, Valentin; Galego, Elói Medina

Some Results on the SchroederBernstein Property for Separable Banach Spaces
We construct a continuum of mutually
nonisomorphic
separable Banach spaces which are complemented in each other.
Consequently, the SchroederBernstein Index of any of these spaces is
$2^{\aleph_0}$. Our
construction is based on a Banach space introduced by W. T. Gowers
and
B. Maurey in 1997.
We also use classical descriptive set theory methods, as in some
work of the first author and C. Rosendal, to improve some results
of P. G. Casazza and
of N. J. Kalton on the
SchroederBernstein Property for
spaces with an unconditional finitedimensional Schauder
decomposition.
Keywords:complemented subspaces,, SchroederBernstein property Categories:46B03, 46B20 

3. CJM 2005 (vol 57 pp. 673)
 Androulakis, G.; Odell, E.; Schlumprecht, Th.; TomczakJaegermann, N.

On the Structure of the Spreading Models of a Banach Space
We study some questions concerning the structure of the
set of spreading models of a separable infinitedimensional Banach
space $X$. In particular we give an example of a reflexive $X$ so that
all spreading models of $X$ contain $\ell_1$ but none of them is
isomorphic to $\ell_1$. We also prove that for any countable set $C$
of spreading models generated by weakly null sequences there is a
spreading model generated by a weakly null sequence which dominates
each element of $C$. In certain cases this ensures that $X$ admits,
for each $\alpha < \omega_1$, a spreading model $(\tilde
x_i^{(\alpha)})_i$ such that if $\alpha < \beta$ then $(\tilde
x_i^{(\alpha)})_i$ is dominated by (and not equivalent to)
$(\tilde x_i^{(\beta)})_i$. Some applications of these ideas are used to
give sufficient conditions on a Banach space for the existence of a
subspace and an operator defined on the subspace, which is not a
compact perturbation of a multiple of the inclusion map.
Category:46B03 

4. CJM 2004 (vol 56 pp. 472)
 Fonf, Vladimir P.; Veselý, Libor

InfiniteDimensional Polyhedrality
This paper deals with generalizations of the notion of a polytope to infinite
dimensions. The most general definition is the following: a bounded closed
convex subset of a Banach space is called a \emph{polytope} if each of its
finitedimensional affine sections is a (standard) polytope.
We study the relationships between eight known definitions
of infinitedimensional
polyhedrality. We provide a complete isometric
classification of them, which gives
solutions to several open problems.
An almost complete isomorphic classification
is given as well (only one implication remains open).
Categories:46B20, 46B03, 46B04, 52B99 

5. CJM 1999 (vol 51 pp. 309)
 Leung, Denny H.; Tang, WeeKee

Symmetric sequence subspaces of $C(\alpha)$, II
If $\alpha$ is an ordinal, then the space of all ordinals less than or
equal to $\alpha$ is a compact Hausdorff space when endowed with the
order topology. Let $C(\alpha)$ be the space of all continuous
realvalued functions defined on the ordinal interval $[0,
\alpha]$. We characterize the symmetric sequence spaces which embed
into $C(\alpha)$ for some countable ordinal $\alpha$. A hierarchy
$(E_\alpha)$ of symmetric sequence spaces is constructed so that, for
each countable ordinal $\alpha$, $E_\alpha$ embeds into
$C(\omega^{\omega^\alpha})$, but does not embed into
$C(\omega^{\omega^\beta})$ for any $\beta < \alpha$.
Categories:03E13, 03E15, 46B03, 46B45, 46E15, 54G12 
