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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 ≤… Click to show full abstract
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.
Keywords:
geometry product;
product spaces;
class;
geometry
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!