Lacunary matrices
Abstract
We study unconditional subsequences of the canonical basis e_rc of elementary matrices in the Schatten class S^p. They form the matrix counterpart to Rudin's Lambda(p) sets of integers in Fourier analysis. In the case of p an even integer, we find a sufficient condition in terms of trails on a bipartite graph. We also establish an optimal density condition and present a random construction of bipartite graphs. As a byproduct, we get a new proof for a theorem of Erdos on circuits in graphs.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2001
 arXiv:
 arXiv:math/0102211
 Bibcode:
 2001math......2211H
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Combinatorics;
 47B10;
 43A46;
 05C38;
 05C80;
 46B15
 EPrint:
 14 pages