This is an announcement for the paper "On generalizations of Gowers norms and their geometry" by Hamed Hatami.

Abstract: Motivated by the definition of the Gowers uniformity norms, we introduce and study a wide class of norms. Our aim is to establish them as a natural generalization of the $L_p$ norms. We shall prove that these normed spaces share many of the nice properties of the $L_p$ spaces. Some examples of these norms are $L_p$ norms, trace norms $S_p$ when $p$ is an even integer, and Gowers uniformity norms. Every such norm is defined through a pair of weighted hypergraphs. In regard to a question of Laszlo Lovasz, we prove several results in the direction of characterizing all hypergraph pairs that correspond to norms.

Archive classification: math.CO math.FA

Mathematics Subject Classification: 46B20, 46E30, 05D99

Remarks: 29 pages

The source file(s), arxiv/ProductNorm17.bbl: 3969 bytes

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