Dichotomy theorems for random matrices and closed ideals of operators on (n=11n)c0
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We prove two dichotomy theorems about sequences of operators into L1 given by random matrices. In the second theorem, we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the corresponding sequence of operators either uniformly factor the identity operators on 1k(k) or uniformly approximately factor through co. The first theorem has a slightly weaker conclusion still related to factorization properties, but makes no assumption on the random matrices. Indeed, it applies to operators defined on an arbitrary sequence of Banach spaces. These results provide information on the closed ideal structure of the Banach algebra of all operators on the space (n=11n)co. 2012 London Mathematical Society.