Geodesic
Unit Preserving Isometries are Homomorphisms in Certain Lp
Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 133-137

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

(a) (ᓂ1 and ᓂ2 will always denote positive bounded measures of equal mass defined on sets X and F respectively. Lp(ᓂ1) and Lp(ᓂ2) will always be complex Lp spaces.(b) M C L∞(ᓂ1) will always denote a subalgebra of L∞(ᓂ1) containing constants.(c) Let be a 1 inear map of ikf into Lp(ᓂ2). We shall say that T is a linear isometry in LP norm if We shall prove the following:THEOREM B. If 2 < p < ∞ and is a linear isometry in the Lp norm with T(l) = 1 then T is a homomorphism on M; that is 
Schneider, Robert. Unit Preserving Isometries are Homomorphisms in Certain Lp. Canadian journal of mathematics, Tome 27 (1975) no. 1, pp. 133-137. doi: 10.4153/CJM-1975-016-7
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[1] 1. Forelli, F., The isometries of HP, Can. J. Math. 16 (1964), 721–728. Google Scholar

[2] 2. Forelli, F., A theorem on isometries and the application of it to the isometries of HP(S) for 2 &lt; p &lt; ∞, Can. J. Math. 25 (1973), 284–289. Google Scholar

[3] 3. Hoffman, K., Banach spaces of analytic functions (Prentice Hall, Englew∞d Cliffs, N.J., 1962). Google Scholar

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