Geodesic
Homological triviality of the category of $L_p$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 3-12

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The paper presents a complete description of topologically injective, topologically surjective, isometric and coisometric multiplication operators by a function acting between $L_p$ spaces of $\sigma$-finite measure spaces. It is proved that all such operators are invertible from the right and left. As a corollary, it is proved that in the category consisting of $L_p$-spaces with all $p\in[1,+\infty]$ considered as left Banach modules over the algebra of bounded measurable functions, all objects are metrically and topologically projective, injective, and flat. 
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     author = {N. T. Nemesh},
     title = {Homological triviality of the category of $L_p$},
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     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a0/}
}
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N. T. Nemesh. Homological triviality of the category of $L_p$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 3-12. http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a0/