1. CJM Online first
 Oikhberg, Timur; Tradacete, Pedro

Almost disjointness preservers
We study the stability of disjointness preservers on Banach lattices.
In many cases, we prove that an "almost disjointness preserving"
operator is well approximable by a disjointness preserving one.
However, this approximation is not always possible, as our
examples show.
Keywords:Banach lattice, disjointness preserving Categories:47B38, 46B42 

2. CJM 2016 (vol 69 pp. 338)
 Garbagnati, Alice

On K3 Surface Quotients of K3 or Abelian Surfaces
The aim of this paper is to prove that a K3 surface is the minimal
model of the quotient of an Abelian surface by a group $G$ (respectively
of a K3 surface by an Abelian group $G$) if and only if a certain
lattice is primitively embedded in its NÃ©ronSeveri group.
This allows one to describe the coarse moduli space of the K3
surfaces which are (rationally) $G$covered by Abelian or K3
surfaces (in the latter case $G$ is an Abelian group).
If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian
surface, this result was already known, so we extend it to the
other cases.
Moreover, we prove that a K3 surface $X_G$ is the minimal model
of the quotient of an Abelian surface by a group $G$ if and only
if a certain configuration of rational curves is present on $X_G$.
Again this result was known only in some special cases, in particular
if $G$ has order 2 or 3.
Keywords:K3 surfaces, Kummer surfaces, Kummer type lattice, quotient surfaces Categories:14J28, 14J50, 14J10 

3. CJM 2013 (vol 66 pp. 1143)
 Plevnik, Lucijan; Šemrl, Peter

Maps Preserving Complementarity of Closed Subspaces of a Hilbert Space
Let $\mathcal{H}$ and $\mathcal{K}$ be infinitedimensional separable
Hilbert spaces and ${\rm Lat}\,\mathcal{H}$ the lattice of all closed subspaces oh $\mathcal{H}$.
We describe the general form of pairs of bijective maps $\phi , \psi :
{\rm Lat}\,\mathcal{H} \to {\rm Lat}\,\mathcal{K}$ having the property that for every pair
$U,V \in {\rm Lat}\,\mathcal{H}$ we have $\mathcal{H} = U \oplus V \iff \mathcal{K} = \phi (U) \oplus \psi (V)$. Then we reformulate this theorem as a description
of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known
structural results for maps on idempotents are easy consequences.
Keywords:Hilbert space, lattice of closed subspaces, complemented subspaces, adjacent subspaces, idempotents Categories:46B20, 47B49 

4. CJM 2010 (vol 62 pp. 870)
 Valdimarsson, Stefán Ingi

The BrascampLieb Polyhedron
A set of necessary and sufficient conditions for the BrascampLieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has corank $1$. This complements the result of Barthe concerning the case where the linear maps all have rank $1$. Pushing our analysis further, we describe the case where the maps have either rank $1$ or rank $2$. A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the BrascampLieb inequality to hold. We present an algorithm which generates such a list.
Keywords:BrascampLieb inequality, LoomisWhitney inequality, lattice, flag Categories:44A35, 14M15, 26D20 

5. 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 

6. CJM 1999 (vol 51 pp. 792)
 Grätzer, G.; Wehrung, F.

Tensor Products and Transferability of Semilattices
In general, the tensor product, $A \otimes B$, of the lattices $A$ and
$B$ with zero is not a lattice (it is only a joinsemilattice with
zero). If $A\otimes B$ is a {\it capped\/} tensor product, then
$A\otimes B$ is a lattice (the converse is not known). In this paper, we
investigate lattices $A$ with zero enjoying the property that $A\otimes
B$ is a capped tensor product, for {\it every\/} lattice $B$ with zero;
we shall call such lattices {\it amenable}.
The first author introduced in 1966 the concept of a {\it sharply
transferable lattice}. In 1972, H.~Gaskill defined,
similarly, sharply transferable semilattices, and characterized them
by a very effective condition (T).
We prove that {\it a finite lattice $A$ is\/} amenable {\it if{}f it is\/}
sharply transferable {\it as a joinsemilattice}.
For a general lattice $A$ with zero, we obtain the result: {\it $A$ is
amenable if{}f $A$ is locally finite and every finite sublattice of $A$
is transferable as a joinsemilattice}.
This yields, for example, that a finite lattice $A$ is amenable
if{}f $A\otimes\FL(3)$ is a lattice if{}f $A$ satisfies (T), with
respect to join. In particular, $M_3\otimes\FL(3)$ is not a lattice.
This solves a problem raised by R.~W.~Quackenbush in 1985 whether
the tensor product of lattices with zero is always a lattice.
Keywords:tensor product, semilattice, lattice, transferability, minimal pair, capped Categories:06B05, 06B15 
