Geodesic
Two remarks concerning the equation $\Pi_p(X,\cdot)=I_p(X,\cdot)$
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XI, Tome 113 (1981), pp. 135-148

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It is proved that the analog of Grothendieck's theorem is valid for a disk-algebra “up to a logarithmic factor”. Namely, if $T\in\mathscr L(C_A,L^1)$ and $\operatorname{rank}T\le n$ then $\pi_2(t)\le C(1+\log n)\|T\|$. The question of whether the logarithmic factor is actually necessary remains open. It is also established that $C^*_A$ is a space of cotype $q$ for any $q$, $q>2$. The proofs are based on a theorem of Mityagin–Pelchinskii: $\pi_p(T)\le c\cdot p\cdot i_p(T)$, $p\ge2$, for any operator $T$ acting from a disk-algebra to an arbitrary Banach space. 
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     author = {S. V. Kislyakov},
     title = {Two remarks concerning the equation $\Pi_p(X,\cdot)=I_p(X,\cdot)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {135--148},
     publisher = {mathdoc},
     volume = {113},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_113_a5/}
}
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S. V. Kislyakov. Two remarks concerning the equation $\Pi_p(X,\cdot)=I_p(X,\cdot)$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XI, Tome 113 (1981), pp. 135-148. http://geodesic.mathdoc.fr/item/ZNSL_1981_113_a5/