Vol. 59, No. 2, 1975

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Norms of random matrices

Grahame Bennett, Victor Wayne Goodman and Charles Michael Newman

Vol. 59 (1975), No. 2, 359–365

Under rather general conditions on the matrix entries, we obtain estimates for the probability distribution of the norm of a random matrix transformation from ln2 to lmq(2 q < ). Asymptotically, the expected norm is remarkably small and this enables us to produce an interesting class of bounded linear operators from l2 to lq. As an application, we complete the characterization of (p,q)-absolutely summing operators on Hilbert space, thereby answering a question left open by several previous authors.

Mathematical Subject Classification 2000
Primary: 15A51
Secondary: 47B99
Received: 20 February 1975
Published: 1 August 1975
Grahame Bennett
Victor Wayne Goodman
Charles Michael Newman