Lacunary matrices
Asma Harcharras, Stefan Neuwirth, Krzysztof Oleszkiewicz
Abstract
We study unconditional subsequences of the canonical basis erc of elementary matrices in the Schatten class Sp. 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.
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