On factorization of nuclear operators through $S_{s,p}$-operators

4 Jul 2021, 10:45


Oleg Reinov


We consider the question of factorizations of products of $l_{r,q}$-nuclear and close operators through the operators of Schatten-Lorentz classes $S_{s,p}(H).$

To get the sharpness of some results, we apply the following generalization of a result of G. Pisier on convolution operators: Given a compact Abelian group $G$ and $f\in C(G),$ the convolution operator $f\!*\cdot: M(G) \to C(G)$ can be factored through an $S_{s,p}$-operator if and only if the set $\hat f$ of Fourier coefficients of $f$ is in $l_{r,q},$ where $1/q=1/p+1, 1/r=1/s+1.$ If $q=r=1,$ we get the result of G. Pisier.

Primary author

Oleg Reinov

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