Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The reconstruction formula for Banach frames and duality   We study conditions on a Banach frame that ensures the validity of a
reconstruction formula. In particular, we show that any Banach frames for (a
subspace of) $L_p$ or $L_{p,q}$ ($1\le p < \infty$) with respect to a solid
sequence space always satisfies an unconditional reconstruction formula. The
existence of reconstruction formulae allows us to prove some James-type results
for atomic decompositions: an unconditional atomic decomposition (or
unconditional Schauder frame) for $X$ is shrinking (respectively, boundedly
complete) if and only if $X$ does not contain an isomorphic copy of $\ell_1$
(respectively, $c_0$).

11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th