Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free and projective generalized multinormed spaces   The paper investigates free and projective ${\bf L}$-spaces, where ${\bf L}$
is a given normed space. These spaces form a far-reaching generalization of
known $p$-multinormed spaces; in particular, if ${\bf L}=L_p(X)$, the ${\bf
L}$-spaces can be considered as $p$-multinormed spaces, based on arbitrary
$\sigma$-finite measure spaces $X$ (for "canonical" $p$-multinormed spaces,
$X=\mathbb N$ with the counting measure). We first describe a "naturally
appearing" functor, based on paving ${\bf L}$ with contractively complemented
finite dimensional subspaces. This finite dimensionality is essential; it
permits us to describe a free ${\bf L}$-space for this functor. As a corollary,
we obtain a wide variety of projective ${\bf L}$-spaces. For "nice" ${\bf L}$
(such as the space of simple $p$-integrable functions on a measure space), we
obtain a full description of projective ${\bf L}$-spaces.

27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc