We present the idea of the construction of Banach spaces with Calkin algebras that are isomorphic to Banach spaces with an unconditional basis (and pointwise multiplication) from a wide class, including $\ell_p$, $1\leq p<\infty$, with the canonical unit vector basis, and $L_p$, $1<p<\infty$, with the Haar system. Joint work with Pavlos Motakis.
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