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 -