Geodesic
For which $p$ and $r$ is the equation $\Pi_p(L^r,\cdot)=I_p(L^r,\cdot)$ true?
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XI, Tome 113 (1981), pp. 237-242 
N. G. Sidorenko. For which $p$ and $r$ is the equation $\Pi_p(L^r,\cdot)=I_p(L^r,\cdot)$ true?. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XI, Tome 113 (1981), pp. 237-242. http://geodesic.mathdoc.fr/item/ZNSL_1981_113_a16/
@article{ZNSL_1981_113_a16,
     author = {N. G. Sidorenko},
     title = {For which~$p$ and~$r$ is the equation $\Pi_p(L^r,\cdot)=I_p(L^r,\cdot)$ true?},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {237--242},
     year = {1981},
     volume = {113},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_113_a16/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is explained when the classes of $p$-absolutely summing and $p$-integral operators given on the space $L^r(\mu)$ coincide. For a Banach space $X$ there is considered the following subset of the real line: $$ J_X\stackrel{\mathrm{def}}=\{p\colon1\le p<\infty,\ \Pi_p(X,Y)=I_p(X,Y)\ \forall Y\}. $$ In the case when $X$ is an infinite-dimensional subspace of the space $L^r(\mu)$, it is proved that $J_X=(1,2]$ if $1\le r\le2$, and $J_X=\{2\}$ if $2 and $X$ is not isomorphic with a Hilbert space.