Nontrivial isometries on sp(α)
sp(α) is a Banach space of sequences x with ‖x‖=(∑i=0∞|xi|p+α∑i=0∞|xi+1−xi|p)1/p. For 1<p<∞, p≠2, 0<α<∞, α≠1, there are no nontrivial surjective isometries in sp(α). It has been conjectured that there are no nontrivial isometries. This note gives two distinct counterexamples to this conj...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171282000222 |
| Summary: | sp(α) is a Banach space of sequences x with ‖x‖=(∑i=0∞|xi|p+α∑i=0∞|xi+1−xi|p)1/p. For 1<p<∞, p≠2, 0<α<∞, α≠1, there are no nontrivial surjective isometries in sp(α). It has been conjectured that there are no nontrivial isometries. This note gives two distinct counterexamples to this conjecture and a partial affirmative answer for the case of isometries with finite codimension. |
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| ISSN: | 0161-1712 1687-0425 |