# [Banach] Abstract of a paper by Marius Junge and Hun Hee Lee

Dale Alspach alspach at www.math.okstate.edu
Fri Jul 6 13:49:08 CDT 2007

This is an announcement for the paper "A Maurey type result for
operator spaces" by Marius Junge and Hun Hee Lee.

Abstract: The little Grothendieck theorem for Banach spaces says
that every bounded linear operator between $C(K)$ and $\ell_2$ is
2-summing. However, it is shown in \cite{J05} that the operator
space analogue fails. Not every cb-map $v : \K \to OH$ is completely
2-summing. In this paper, we show an operator space analogue of
Maurey's theorem : Every cb-map $v : \K \to OH$ is $(q,cb)$-summing
for any $q>2$ and hence admits a factorization $\|v(x)\| \leq c(q) \|v\|_{cb} \|axb\|_q$ with $a,b$ in the unit ball of the Schatten
class $S_{2q}$.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 47L25; 46B07

Remarks: 29 pages

The source file(s), MaureyTypeResultOS.tex: 99707 bytes, is(are)
stored in gzipped form as 0707.0152.gz with size 25kb. The corresponding
postcript file has gzipped size 184kb.

Submitted from: lee.hunhee at gmail.com

The paper may be downloaded from the archive by web browser from
URL

http://front.math.ucdavis.edu/0707.0152

or

http://arXiv.org/abs/0707.0152

or by email in unzipped form by transmitting an empty message with
subject line

uget 0707.0152

or in gzipped form by using subject line

get 0707.0152

to: math at arXiv.org.