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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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 |
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doaj-6c1840db4ced4d898e79d48077219db82020-11-24T23:01:34ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015225726110.1155/S0161171282000222Nontrivial isometries on sp(α)Stephen L. Campbell0Department of Mathematics, North Carolina State University, Raleigh 27650, North Carolina, USAsp(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.http://dx.doi.org/10.1155/S0161171282000222isometrysequential Banach spaceBanach space. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Stephen L. Campbell |
| spellingShingle |
Stephen L. Campbell Nontrivial isometries on sp(α) International Journal of Mathematics and Mathematical Sciences isometry sequential Banach space Banach space. |
| author_facet |
Stephen L. Campbell |
| author_sort |
Stephen L. Campbell |
| title |
Nontrivial isometries on sp(α) |
| title_short |
Nontrivial isometries on sp(α) |
| title_full |
Nontrivial isometries on sp(α) |
| title_fullStr |
Nontrivial isometries on sp(α) |
| title_full_unstemmed |
Nontrivial isometries on sp(α) |
| title_sort |
nontrivial isometries on sp(α) |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1982-01-01 |
| description |
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. |
| topic |
isometry sequential Banach space Banach space. |
| url |
http://dx.doi.org/10.1155/S0161171282000222 |
| work_keys_str_mv |
AT stephenlcampbell nontrivialisometriesonspa |
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1725639149313064960 |