Geodesic
A note on mutiplication operators on Köthe-Bochner spaces
Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 141-142 
S. S. Khurana; S. S. Khurana. A note on mutiplication operators on Köthe-Bochner spaces. Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 141-142. http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a12/
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     author = {S. S. Khurana and S. S. Khurana},
     title = { A note on mutiplication operators on {K\"othe-Bochner} spaces},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {141--142},
     year = {2012},
     volume = {81},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a12/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let (Ω, A, μ) is a finite measure space, E an order continuous Banach function space over μ, X a Banach space and E(X) the Köthe-Bochner space. A new simple proof is given of the result that a continuous linear operator T: E(X) ® E(X) is a multiplication operator (by a function in L¥) iff T(g < f, x* > x) =g < T(f), x* > x for every g Î L¥, f Î E(X), x Î X, x* Î X*.