论文信息 - Geometry of product spaces

Geometry of product spaces

Abstract We study the inheritance of some geometric properties in a class of normed subspaces of products of normed spaces. This class includes the standard p-direct sums for 1 ≤ p ≤ ∞ . We obtain necessary conditions for a space of this class to be (1) n-uniformly rotund, (2) n-uniformly rotund relative to every n-dimensional subspace and (3) n-rotund for some positive integer n. In each of the three cases, we identify a subclass such that the same conditions are sufficient for a member to have the corresponding property.

M. Veena Sangeetha | M. Sangeetha

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