Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometry of integral polynomials, $M$-ideals and unique norm preserving
  extensions   We use the Aron-Berner extension to prove that the set of extreme points of
the unit ball of the space of integral polynomials over a real Banach space $X$
is $\{\pm \phi^k: \phi \in X^*, \| \phi\|=1\}$. With this description we show
that, for real Banach spaces $X$ and $Y$, if $X$ is a non trivial $M$-ideal in
$Y$, then $\hat\bigotimes^{k,s}_{\epsilon_{k,s}} X$ (the $k$-th symmetric
tensor product of $X$ endowed with the injective symmetric tensor norm) is
\emph{never} an $M$-ideal in $\hat\bigotimes^{k,s}_{\epsilon_{k,s}} Y$. This
result marks up a difference with the behavior of non-symmetric tensors since,
when $X$ is an $M$-ideal in $Y$, it is known that
$\hat\bigotimes^k_{\epsilon_k} X$ (the $k$-th tensor product of $X$ endowed
with the injective tensor norm) is an $M$-ideal in
$\hat\bigotimes^k_{\epsilon_k} Y$. Nevertheless, if $X$ is Asplund, we prove
that every integral $k$-homogeneous polynomial in $X$ has a unique extension to
$Y$ that preserves the integral norm. We explicitly describe this extension.
  We also give necessary and sufficient conditions (related with the continuity
of the Aron-Berner extension morphism) for a fixed $k$-homogeneous polynomial
$P$ belonging to a maximal polynomial ideal $\Q(^kX)$ to have a unique norm
preserving extension to $\Q(^kX^{**})$. To this end, we study the relationship
between the bidual of the symmetric tensor product of a Banach space and the
symmetric tensor product of its bidual and show (in the presence of the BAP)
that both spaces have `the same local structure'. Other applications to the
metric and isomorphic theory of symmetric tensor products and polynomial ideals
are also given.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga