Extreme flatness and Hahn-Banach type theorems for normed modules over c_0

Details Extreme flatness and Hahn-Banach type theorems for normed modules over c_0 Extreme flatness and Hahn-Banach type theorems for normed modules over c_0

2010-05-04

arxiv.org/abs/1005.0489v1

Mathematics

Functional Analysis

Scientific paper

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

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