Bounded Sequences,Orbits and Invariant Subspaces |
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Authors: | Driss Drissi |
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Institution: | 1.Department of Mathematics and Computer Science,Kuwait University,Safat,Kuwait |
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Abstract: | Let {x n } be a sequence of complex numbers and let \({\Delta^nx_j = \sum\nolimits_{k=0}^{n} (-1)^k\break\left(\begin{array}{l}n\\ k\\\end{array} \right)x_{n-k+j}}\) . In this paper, we will show that if \({ |x_n| = O(n^k)}\) , as n → ∞ for some positive integer k, and \({n|\Delta^n x_j|^{\frac{1}{n}} \to 0}\) as n→ ∞, then \({\Delta^{k+1} x_j = 0}\) . More importantly, applications to the orbits of operators and invariant subspace problem are also given; this helps to improve former results obtained by Gelfand–Hille, Mbekhta–Zemánek and others. |
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