Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representing non-weakly compact operators   For each $S \in L(E)$ (with $E$ a Banach space) the operator $R(S) \in
L(E^{**}/E)$ is defined by $R(S)(x^{**}+E) = S^{**}x^{**}+E$ \quad ($x^{**}\in
E^{**}$). We study mapping properties of the correspondence $S\to R(S),$ which
provides a representation $R$ of the weak Calkin algebra $L(E)/W(E)$ (here
$W(E)$ denotes the weakly compact operators on $E$). Our results display
strongly varying behaviour of $R.$ For instance, there are no non--zero compact
operators in Im$(R)$ in the case of $L^1$ and $C(0,1),$ but $R(L(E)/W(E))$
identifies isometrically with the class of lattice regular operators on
$\ell^2$ for $E=\ell^2(J)$ (here $J$ is the James' space). Accordingly, there
is an operator $T \in L(\ell^2(J))$ such that $R(T)$ is invertible but $T$
fails to be invertible modulo $W(\ell^2(J)).$

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs