Operators factorable through Lorentz sequence spaces

Weestablishkeyresultsandproperties of the Banach space of vector-valued weakly Lorentz sequence, denoted p,qʷ(·). These results extend a classical result due to Grothendieck for ₚ-spaces to the Lorentz setting. Additionally, we introduce and study a new concept, namelyp,q-factorable operators. We establish fundamental properties of this class and provide a characterization of p,q-factorable operators. Specifically, we show that an operator T between Banach spaces is p,q-factorable if and only if it admits a continuous linear factorization through the Lorentz space p,q.