Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extreme flatness and Hahn-Banach type theorems for normed modules over
  c_0   Let A be a commutative normed algebra, K a class of normed A-modules. A
normed A-module Z is called extremely flat with respect to K, if, for every
isometric morphism of normed A-modules, belonging to K, the non-completed
projective A-module tensor product of this morphism and the identity morphism
on Z, is also isometric. In the present paper we take, in the capacity of A,
the algebra c_0 of vanishing sequences and consider the class of the so-called
homogeneous modules, over the latter algebra, denoted by H. The main theorem
gives a full description of essential homogeneous modules over the mentioned
algebra that are extremely flat with respect to H. (In particular, all
l_p-sums; p<infinity of normed spaces of integrable functions on different
measure spaces have the indicated property). As a corollary, some theorems of
Hahn-Banach type, concerning extensions of c_0-module morphisms with
preservation of their norms, are obtained. (In particular, l_p-sums of normed
spaces of essentially bounded functions play, in the relevant context, the same
role as the scalar field in the classical Hahn-Banach Theorem). Besides, the
following related result is established. If I is a topologically injective
morphism of normed c_0-modules, then for every normed c_0-module Z, the
non-completed projective tensor product of I and the identity morphism on Z is
also injective (despite it is, generally speaking, not topologically
injective). If I is a (just) injective bounded morphism, then such a tensor
product is not bound to be injective. Finally, it is shown that we can not omit
the word "essential" in the formulation of the main theorem. Namely, the
non-essential homogeneous c_0-module of all bounded sequences is not extremely
flat with respect to H.

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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org