Interpolator Symmetries and New Kalton-Peck Spaces

We study the six diagrams generated by the first three Schechter interpolators Δ ₂(f)= f''(1/2)/2!, Δ ₁(f)= f'(1/2), Δ ₀(f)=f(1/2) Δ 2 ( f ) = f ′ ′ ( 1 / 2 ) / 2 ! , Δ 1 ( f ) = f ′ ( 1 / 2 ) , Δ 0 ( f ) = f ( 1 / 2 ) acting on the Calderón space associated to the pair ( _∞ , ₁) ( ℓ ∞ , ℓ 1 ) . We will study the remarkable and somehow unexpected properties of all the spaces appearing in those diagrams: two new spaces (and their duals), two Orlicz spaces (and their duals) in addition to the third order Rochberg space, the standard Kalton-Peck space Z₂ Z 2 and, of course, the Hilbert space ₂ ℓ 2 . We will also deal with a nice test case: that of weighted ₂ ℓ 2 spaces, in which case all involved spaces are Hilbert spaces.