Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order continuous extensions of positive compact operators on Banach
  lattices   Let $E$ and $F$ be Banach lattices. Let $G$ be a vector sublattice of $E$ and
$T: G\rightarrow F$ be an order continuous positive compact (resp. weakly
compact) operators. We show that if $G$ is an ideal or an order dense
sublattice of $E$, then $T$ has a norm preserving compact (resp. weakly
compact) positive extension to $E$ which is likewise order continuous on $E$.
In particular, we prove that every compact positive orthomorphism on an order
dense sublattice of $E$ extends uniquely to a compact positive orthomorphism on
$E$.

20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex