Abstract
It is proved that the analog of Grothendieck's theorem is valid for a diskalgebra “up to a logarithmic factor.” Namely, if Tεℒ (CA, L1) and then π2(T)⩽C (1+logn) ¦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: πp(T)⩽C·p·ip(T), p⩾2 for any operator T acting from a disk-algebra to an arbitrary Banach space.
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