[Banach] Abstract of a paper by Joel A. Tropp
alspach at www.math.okstate.edu
Wed Dec 6 06:21:48 CST 2006
This is an announcement for the paper "A new proof of the paving
property for uniformly bounded matrices" by Joel A. Tropp.
Abstract: This note presents a new proof of an important result due
to Bourgain and Tzafriri that provides a partial solution to the
Kadison--Singer problem. The result shows that every unit-norm
matrix whose entries are relatively small in comparison with its
dimension can be paved by a partition of constant size. That is,
the coordinates can be partitioned into a constant number of blocks
so that the restriction of the matrix to each block of coordinates
has norm less than one half. The original proof of Bourgain and
Tzafriri involves a long, delicate calculation. The new proof relies
on the systematic use of symmetrization and Khintchine inequalities
to estimate the norm of some random matrices. The key new ideas are
due to Rudelson.
Archive classification: Metric Geometry; Functional Analysis;
Mathematics Subject Classification: 46B07; 47A11; 15A52
Remarks: 12 pages
The source file(s), bdd-ks-v1.bbl: 2693 bytes, bdd-ks-v1.tex: 41646
bytes, macro-file.tex: 8551 bytes, is(are) stored in gzipped form
as 0612070.tar.gz with size 15kb. The corresponding postcript file
has gzipped size 99kb.
Submitted from: jtropp at umich.edu
The paper may be downloaded from the archive by web browser from
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to: math at arXiv.org.
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