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Recently, Jawerth, Rochberg and Weiss have studied nonlinear maps arising from interpolation theory which satisfy commutator relationships with interpolated linear operators. Here we present a very general result of this type for rearrangement-invariant Banach function spaces.
Those families of (closed) subspaces of a (real or complex) Banach space that arise as the set of atoms of an atomic Boolean algebra subspace lattice, abbreviated ABSL, are characterized. This characterization is used to obtain new examples of ABSL's including some with one-dime…
