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Weak statistical convergence and weak filter convergence for unbounded sequences

机译:无界序列的弱统计收敛和弱滤波收敛

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摘要

For every weakly statistically convergent sequence (x_n) with increasing norms in a Hilbert space we prove that sup_n{short parallel}x_n{short parallel}/√n < ∞. This estimate is sharp. We study analogous problem for some other types of weak filter convergence, in particular for the Erd?s-Ulam filters, analytical P-filters and F_σ filters. We present also a refinement of the recent Aron-Garcia-Maestre result on weakly dense sequences that tend to infinity in norm.
机译:对于希尔伯特空间中范数增加的每个弱统计收敛序列(x_n),我们证明sup_n {short parallel} x_n {short parallel} /√n<∞。这个估计很准确。我们研究了一些其他类型的弱滤波器收敛性的类似问题,特别是对于Erd?s-Ulam滤波器,解析P滤波器和F_σ滤波器。我们还提出了对最近的Aron-Garcia-Maestre结果的改进,该结果在标准上趋于无穷的弱密集序列上。

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