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We present a new approach to Lorentz-Shimogaki and Arazy-Cwikel Theoremswhich covers all range of $p,q\in (0,\infty]$ for function spaces and sequencespaces. As a byproduct, we solve a conjecture of Levitina and the last twoauthors.

Lorentz-Shimogaki-Arazy-Cwikel Theorem Revisited