Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complemented Subspaces of L_p Determined by Partitions and Weights   Many of the known complemented subspaces of L_p have realizations as sequence
spaces. In this paper a systematic approach to defining these spaces which uses
partitions and weights is introduced. This approach gives a unified description
of many well-known complemented subspaces of L_p. It is proved that the class
of spaces with such norms is stable under (p,2) sums. By introducing the notion
of an envelope norm, we obtain a necessary condition for a Banach sequence
space with norm given by partitions and weights to be isomorphic to a subspace
of L_p. Using this we define a space Y_n with norm given by partitions and
weights with distance to any subspace of L_p growing with n. This allows us to
construct an example of a Banach space with norm given by partitions and
weights which is not isomorphic to a subspace of L_p.

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The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con