1. CJM Online first
 Astashkin, Sergey V.; Lesnik, Karol; Maligranda, Lech

Isomorphic structure of CesÃ ro and Tandori spaces
We investigate the isomorphic structure of the CesÃ ro spaces
and their duals, the Tandori spaces.
The main result states that the CesÃ ro function space $Ces_{\infty}$
and its sequence counterpart
$ces_{\infty}$ are isomorphic, which answers the question posted
previously.
This is rather surprising
since $Ces_{\infty}$ (like the known Talagrand's example)
has no natural lattice predual.
We prove that $ces_{\infty}$ is not isomorphic to ${\ell}_{\infty}$
nor is $Ces_{\infty}$ isomorphic to the
Tandori space $\widetilde{L_1}$ with the norm $\f\_{\widetilde{L_1}}=
\\widetilde{f}\_{L_1},$ where
$\widetilde{f}(t):= \operatorname{esssup}_{s \geq t} f(s).$ Our investigation
involves also an examination of the
Schur and DunfordPettis properties of CesÃ ro and Tandori
spaces.
In particular, using results of Bourgain we show that a wide
class of CesÃ roMarcinkiewicz and
CesÃ roLorentz spaces have the latter property.
Keywords:CesÃ ro and Tandori sequence spaces, CesÃ ro and Tandori function spaces, CesÃ ro operator, Banach ideal space, symmetric space, Schur property, DunfordPettis property, isomorphism Categories:46E30, 46B20, 46B42, 46B45 

2. CJM 2007 (vol 59 pp. 614)
 Labuschagne, C. C. A.

Preduals and Nuclear Operators Associated with Bounded, $p$Convex, $p$Concave and Positive $p$Summing Operators
We use Krivine's form of the Grothendieck inequality
to renorm the space of bounded linear maps acting between Banach
lattices. We
construct preduals and describe the nuclear operators
associated with these preduals for this renormed space
of bounded operators as well as for
the spaces of $p$convex,
$p$concave and positive $p$summing operators acting
between Banach lattices and Banach spaces.
The nuclear operators obtained are described in
terms of factorizations through
classical Banach spaces via positive operators.
Keywords:$p$convex operator, $p$concave operator, $p$summing operator, Banach space, Banach lattice, nuclear operator, sequence space Categories:46B28, 47B10, 46B42, 46B45 

3. 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 

4. CJM 1997 (vol 49 pp. 1242)
 Randrianantoanina, Beata

$1$complemented subspaces of spaces with $1$unconditional bases
We prove that if $X$ is a complex strictly monotone sequence
space with $1$un\con\di\tion\al basis, $Y \subseteq X$ has no bands
isometric to $\ell_2^2$ and $Y$ is the range of normone projection from
$X$, then $Y$ is a closed linear span a family of mutually
disjoint vectors in $X$.
We completely characterize $1$complemented subspaces and normone
projections in complex spaces $\ell_p(\ell_q)$ for $1 \leq p, q <
\infty$.
Finally we give a full description of the subspaces that are spanned
by a family of disjointly supported vectors and which are
$1$complemented in (real or complex) Orlicz or Lorentz sequence
spaces. In particular if an Orlicz or
Lorentz space $X$ is not isomorphic to $\ell_p$ for some $1 \leq p <
\infty$ then the only subspaces
of $X$ which are $1$complemented and disjointly supported are the
closed linear spans of block bases with constant
coefficients.
Categories:46B20, 46B45, 41A65 
