# Nonlinear Nuclear Operators ?

Is there a "right" definition of the nuclear operator in the nonlinear framework ? Of course, such an operator must be compact, while a linear operator should be "nonlinearly" nuclear iff it is nuclear as usual. [These are naive conditions, of course.] Since here the Frechet derivative is useless. For example, the "cubing" self-map of $\ell^{2}$, i.e., $(x_{n})$ $\rightarrow\(x_{n}^{3})$ , has nuclear derivative at each point, yet it is clearly noncompact. OTOH, it seems that a [nonlinear] Lipschitz $p$-summing operator need not to be power compact. Some thoughts ?

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