Geodesic
Isometries of sp (α)
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 59-67

Voir la notice de l'article provenant de la source Cambridge University Press

Let l < p < ∞, p ≠ 2 and α > 0. In what follows s p (α) will denote the space of all real or complex sequences for which (1.1) In this paper we show that the spaces s p (α) are Banach spaces under the natural norm and in fact share many properties that the usual l p spaces have. Our main results give characterizations of the surjective isometries of s p (α). These turn out to be quite different than the results for l p . For example, we show that for α ≠ 1, an operator T is a surjective isometry if and only if T is a modulus one multiple of the identity. The methods used are valid for both real and complex scalars. They involve the use of a disjoint support condition together with a property of semi inner products. In the complex case the information on isometries allows us to give complete descriptions of the Hermitian operators as well as the adjoint abelian operators. 
Fleming, R. J.; Jamison, J. E. Isometries of sp (α). Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 59-67. doi: 10.4153/CJM-1981-007-4
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