On summability of bilinear operators

DANIEL CARANDO; VERÓNICA DIMANT

MATHEMATISCHE NACHRICHTEN

Año: 2003 vol. 259 p. 3 - 11

0025-584X

We study some properties of strongly and absolutely $p-$summing bilinearoperators. We show that Hilbert-Schmidt bilinear mappings are both stronglyand absolutely $p-$summing, for every $p\geq 1.$ Giving an example of astrongly $1-$summing bilinear mapping which fails to be weakly compact, weanswer a question posed in \cite{D1}. We prove that, as in the linear case,every bilinear operator from ${\cal L}_{\infty }-$spaces to an ${\cal L}%_{2}- $space is absolutely $2-$summing.