TY - JOUR

T1 - Norms of random matrices

AU - Bennett, G.

AU - Goodman, V.

AU - Newman, C. M.

PY - 1975/8

Y1 - 1975/8

N2 - Under rather general conditions on the matrix entries, we obtain estimates for the probability distribution of the norm of a random matrix transformation from l2 to lq (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.

AB - Under rather general conditions on the matrix entries, we obtain estimates for the probability distribution of the norm of a random matrix transformation from l2 to lq (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.

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U2 - 10.2140/pjm.1975.59.359

DO - 10.2140/pjm.1975.59.359

M3 - Article

AN - SCOPUS:84972549296

SN - 0030-8730

VL - 59

SP - 359

EP - 365

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -