Compact operators into the spaces of strongly C₁ summable and bounded sequences

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• 作者：Eberhard Malkowsky^a ; ^{ema@Bankerinter.net"" rel=""nofollow} ; Ivana Djolović ; ^b ; ^{zucko@open.telekom.rs"" rel=""nofollow} ; ^{zucko@nadlanu.com"" rel=""nofollow}
• 关键词：Strongly bounded and summable sequences ; Matrix transformations ; Compact operators ; Cesà ; ro method
• 刊名：Nonlinear Analysis
• 出版年：2011
• 出版时间：July 2011
• 年：2011
• 卷：74
• 期：11
• 页码：3736-3750
• 全文大小：328 K

文摘

We establish the necessary and sufficient conditions for the entries of an infinite matrix to map any of the classical sequence spaces ℓ_p(1≤p≤∞), c₀ and c into the spaces w₀, w and w_∞ of all sequences that are strongly summable to zero, strongly summable and strongly bounded, by the Cesàro method of order 1. We also give the representations of the general bounded linear operators from c into any of the spaces w₀, w and w_∞, and compute or estimate the Hausdorff measure of noncompactness in each case. Finally, we apply our results to characterise the compact linear operators between the spaces mentioned above, and generalise two classical results by Steinhaus (1911) [5], Maddox (1967) [31], and Cohen and Dunford (1937) [24].