I have the following question: does the Lorentz spaces $\Lambda(w,1)$ have nontrivial cotype and admit an unconditional basis(or even a symmetric basis)?Thank you.



Does the Lorentz spaces $\Lambda(w,1)$ have nontrivial cotype?
I think that your question about cotype is answered in S. Reisner, Ann. Inst. Fourier, Grenoble 31 (1981), 239-255 (see Theorem 2). 


