[Banach] Abstract of a paper by Hun Hee Lee

This is an announcement for the paper "Unconditionality with respect to orthonormal systems in noncommutative $L_2$ spaces" by Hun Hee Lee.

Abstract: Orthonormal systems in commutative $L_2$ spaces can be used to classify Banach spaces. When the system is complete and satisfies certain norm condition the unconditionality with respect to the system characterizes Hilbert spaces. As a noncommutative analogue we introduce the notion of unconditionality of operator spaces with respect to orthonormal systems in noncommutative $L_2$ spaces and show that the unconditionality characterizes operator Hilbert spaces when the system is complete and satisfy certain norm condition. The proof of the main result heavily depends on free probabilistic tools such as contraction principle for $*$-free Haar unitaries, comparision of averages with respect to $*$-free Haar unitaries and $*$-free circular elements and $K$-covexity, type 2 and cotype 2 with respect to $*$-free circular elements.

Archive classification: Functional Analysis; Operator Algebras

Mathematics Subject Classification: 47L25; 46L53

Remarks: 18 pages

The source file(s), Unc-NoncomONS.tex: 56149 bytes, is(are) stored in gzipped form as 0610245.gz with size 15kb. The corresponding postcript file has gzipped size 92kb.

Submitted from: lee.hunhee@gmail.com

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

http://front.math.ucdavis.edu/math.FA/0610245

or

http://arXiv.org/abs/math.FA/0610245

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

uget 0610245

or in gzipped form by using subject line

get 0610245

to: math@arXiv.org.