Norms of random matrices

G. Bennett, V. Goodman, C. M. Newman

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)359-365
Number of pages7
JournalPacific Journal of Mathematics
Volume59
Issue number2
DOIs
StatePublished - Aug 1975

ASJC Scopus subject areas

  • Mathematics(all)

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