On the divergence of series of the form \sum_{k=1}^\infty\|A_k x\|^p

Let {A} be a system of operators. With any element x we associate the set of elements {Ax}. We study conditions under which there exists an element x such that the sum of p-th powers of norms of the elements {Ax} is equal to infinity.

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Bibliographic Details
Published in:arXiv.org 2012-08
Main Author: Feshchenko, Ivan
Format: Article
Language:English
Subjects:
Divergence
Norms
Online Access:Get full text
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Summary:Let {A} be a system of operators. With any element x we associate the set of elements {Ax}. We study conditions under which there exists an element x such that the sum of p-th powers of norms of the elements {Ax} is equal to infinity.
ISSN:2331-8422