Nontrivial isometries on s p ( α )

Stephen L. Campbell

International Journal of Mathematics and Mathematical Sciences, 1982, vol. 5, 1-5

Abstract:

s p ( α ) is a Banach space of sequences x with ‖ x ‖ = ( ∑ i = 0 ∞ | x i | p + α ∑ i = 0 ∞ | x i + 1 − x i | p ) 1 / p . For 1 < p < ∞ , p ≠ 2 , 0 < α < ∞ , α ≠ 1 , there are no nontrivial surjective isometries in s p ( 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.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:108097

DOI: 10.1155/S0161171282000222

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