Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Grothendieck properties   A Banach space $E$ has the Grothendieck property if every (linear bounded)
operator from $E$ into $c_0$ is weakly compact. It is proved that, for an
integer $k>1$, every $k$-homogeneous polynomial from $E$ into $c_0$ is weakly
compact if and only if the space ${\cal P}(^kE)$ of scalar valued polynomials
on $E$ is reflexive. This is equivalent to the symmetric $k$-fold projective
tensor product of $E$ (i.e., the predual of ${\cal P}(^kE)$) having the
Grothendieck property. The Grothendieck property of the projective tensor
product $E\widehat{\bigotimes}F$ is also characterized. Moreover, the
Grothendieck property of $E$ is described in terms of sequences of polynomials.
  Finally, it is shown that if every operator from $E$ into $c_0$ is completely
continuous, then so is every polynomial between these spaces.

12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics