On a summability theorem of Berg, Crawford and Whitley
1972 ◽
Vol 71
(3)
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pp. 495-497
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Keyword(s):
We recall that a matrix A is said to sum a sequence x if Axε c, the space of all convergent sequences, and that A is conservative if it sums every convergent sequence. If A is conservative, A defines a continuous linear operator on c. Berg (2), Crawford (3)and Whitley (9) have proved the following theorem:Theorem 1. A conservative matrix sums no bounded divergent sequence if and only if,considered as an operator on c, it is range closed and has finite-dimensional null-spac
1983 ◽
Vol 26
(2)
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pp. 163-167
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Keyword(s):
2011 ◽
Vol 14
(01)
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pp. 1-14
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Keyword(s):
1987 ◽
Vol 29
(2)
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pp. 271-273
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2001 ◽
Vol 14
(3)
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pp. 303-308
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1972 ◽
Vol 7
(2)
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pp. 183-190
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Keyword(s):
2002 ◽
Vol 66
(3)
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pp. 425-441
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