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

Ivan Feshchenko

arxiv: 1208.1863 · v1 · pith:UIFLEF7Enew · submitted 2012-08-09 · 🧮 math.FA

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

Ivan Feshchenko This is my paper

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keywords elementelementsassociateconditionsdivergenceequalexistsform

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

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