The random paving property for uniformly bounded matrices

Joel A. Tropp. "The random paving property for uniformly bounded matrices." Studia Mathematica 185.1 (2008): 67-82. <http://eudml.org/doc/284845>.

@article{JoelA2008,
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 (noncommutative) Khinchin inequalities to estimate the norms of some random matrices.},
author = {Joel A. Tropp},
journal = {Studia Mathematica},
keywords = {Kadison-Singer problem; paving problem; random matrix},
language = {eng},
number = {1},
pages = {67-82},
title = {The random paving property for uniformly bounded matrices},
url = {http://eudml.org/doc/284845},
volume = {185},
year = {2008},
}

TY - JOUR
AU - Joel A. Tropp
TI - The random paving property for uniformly bounded matrices
JO - Studia Mathematica
PY - 2008
VL - 185
IS - 1
SP - 67
EP - 82
AB - 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 (noncommutative) Khinchin inequalities to estimate the norms of some random matrices.
LA - eng
KW - Kadison-Singer problem; paving problem; random matrix
UR - http://eudml.org/doc/284845
ER -