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- W2000633313 abstract "Necessary and sufficient conditions are given for an infinite matrix to sum all bounded strongly summable sequences. It is shown that the Borel matrix does not sum all such sequences. A corollary is that the bounded summability field of the Borel method is strictly contained in that of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper C comma 1 right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(C,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> method. Also, it is proved that no coregular matrix can almost sum all bounded sequences—a generalization of Steinhaus’ theorem." @default.
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- W2000633313 date "1974-01-01" @default.
- W2000633313 modified "2023-10-13" @default.
- W2000633313 title "Steinhaus type theorems for summability matrices" @default.
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- W2000633313 doi "https://doi.org/10.1090/s0002-9939-1974-0364938-0" @default.
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