Complex interpolation of families of Orlicz sequence spaces (Q2218727)

This is a very fine paper that develops the theory of complex interpolation for families of Orlicz sequence spaces and uses it to make a few valuable additions to \textit{N.~J. Kalton}'s theorem [Trans. Am. Math. Soc. 333, No.~2, 479--529 (1992; Zbl 0776.46033)]. More precisely: \begin{itemize} \item[1.] Kalton's extraordinary theorem established the connection between complex interpolation scales and centralizers on Köthe spaces. It has a coda: real centralizers appear as derivations from scales of two Köthe spaces, while general centralizers seem to require three Köthe spaces. \item[2.] The author addresses the question: is three actually necessary? Could it be always two? \item[3.] The answer is no, two are not enough for ``abstract'' reasons. This is the content of Section~3. \item[4.] The author goes beyond that: why not producing an explicit example? This is not so easy as it sounds: scales of \(\ell_p\) spaces or Lorentz spaces \(\ell_{p,q}\) are not enough to provide such an example. So he moves to Orlicz spaces. \item[5.] The author presents an extremely nice treatise on complex interpolation for families of Orlicz sequence spaces. \item[6.] And then the explicit counterexample: a family of three Orlicz sequence spaces generating a centralizer at \(\ell_2\) that cannot be obtained from two Köthe spaces. \end{itemize} It is curious how a conceptually ``plain'' example, from the abstract approach, can be so technically demanding from the specific point of view. The reason seems to be hidden in the number~3 and the requirement of making the example with a ``small'' class of spaces. Thus, the paper casts a good number of questions and ideas.