Some Compact Operators on the Hahn Space
Keyword(s):
We establish the characterisations of the classes of bounded linear operators from the generalised Hahn sequence space $h_{d}$, where $d$ is an unbounded monotone increasing sequence of positive real numbers, into the spaces $[c_{0}]$, $[c]$ and $[c_{\infty}]$ of sequences that are strongly convergent to zero, strongly convergent and strongly bounded. Furthermore, we prove estimates for the Hausdorff measure of noncompactness of bounded linear operators from $h_{d}$ into $[c]$, and identities for the Hausdorff measure of noncompactness of bounded linear operators from $h_{d}$ to $[c_{0}]$, and use these results to characterise the classes of compact operators from $h_{d}$ to $[c]$ and $[c_{0}]$.
1974 ◽
Vol 26
(1)
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pp. 115-120
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1982 ◽
Vol 25
(1)
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pp. 78-81
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1980 ◽
Vol 21
(1)
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pp. 75-79
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1989 ◽
Vol 32
(4)
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pp. 434-440
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