  Transverse polarization of Lambda hyperons produced in p p and p Pb
collisions is discussed. A factorized description in the intermediate to high
p_T region is considered that involves transverse momentum and spin dependence
in the fragmentation process. Consequences and suggestions for investigations
at LHC are pointed out for the process p + p -> Lambda^uparrow + jets + X at
midrapidity and p + p/Pb -> Lambda^uparrow + X in the forward region.
