On Pitt's theorem for operators between scalar and vector-valued quasi-Banach sequence spaces
This article presents extensions of the classical theorem of Pitt about the compactness of all operators from \(\ell_p\) into \(\ell_q\) if \(p> q\) to a wide class of quasi-Banach sequence spaces. Applications are given to quasi-normed Minkowski, Lorentz and Orlicz sequence spaces. The proofs are based on gliding hump methods. The case of Banach spaces of vector valued sequences is also treated. Several results are improved in the last section by use of an extension of the Maurey-Rosenthal factorization theory for operators between Banach sequence spaces, thus showing that the compact operators in fact factorize through suitable \(\ell_p\)-spaces.
quasi-normed Minkowski, Lorentz and Orlicz sequence spaces
scientific article; zbMATH DE number 1466223