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

Abstract

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.

arXiv comment9 pages, submitted to Studia Mathematica