Randomized Operators on $${n\times n}$$ n × n Matrices and Applications

Abstract

Some combinatorial and probabilistic estimates motivated by earlier works due to S. Kwapien and C. Schutt are proved. We study these estimates in the general setting of rearrangement invariant function and sequence spaces and identify the class of function spaces in which such estimates hold. We demonstrate the sharpness of our results and present some applications, one of which is an alternative proof of a familiar Raynaud–Schutt theorem describing symmetric subspaces in \({L_1}\).