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- W4245197817 abstract "We study the spaces<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mn>0</mml:mn><mml:mi>p</mml:mi></mml:msubsup></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mi>∞</mml:mi><mml:mi>p</mml:mi></mml:msubsup></mml:mrow></mml:math>of sequences that are strongly summable to 0, summable, and bounded with index<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>p</mml:mi><mml:mo>≥</mml:mo><mml:mn>1</mml:mn></mml:math>by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>into the spaces<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mi>∞</mml:mi><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math>, and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mn>0</mml:mn><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:math>. We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mn>0</mml:mn><mml:mi>p</mml:mi></mml:msubsup></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mi>p</mml:mi></mml:msup></mml:mrow></mml:math>into<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M13><mml:mrow><mml:msubsup><mml:mi>w</mml:mi><mml:mn>0</mml:mn><mml:mn>1</mml:mn></mml:msubsup></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M14><mml:mrow><mml:msup><mml:mi>w</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math>." @default.
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- W4245197817 date "2014-01-01" @default.
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- W4245197817 title "Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces" @default.
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- W4245197817 doi "https://doi.org/10.1155/2014/196489" @default.
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