Quantitative coarse embeddings of quasi-Banach spaces into a Hilbert space

2015/11/16 by Michal Kraus, Kraus, Michal
Mathematics · #46A16 #46B20 #46B85 #51F99 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46A16 #msc:46B20 #msc:46B85 #msc:51F99

paper · pdf · doi:10.48550/arxiv.1511.05214

11 pages

arxiv created 2015/11/16 · arxiv updated 2015/11/18

Abstract

We study how well a quasi-Banach space can be coarsely embedded into a Hilbert space. Given any quasi-Banach space X which coarsely embeds into a Hilbert space, we compute its Hilbert space compression exponent. We also show that the Hilbert space compression exponent of X is equal to the supremum of the amounts of snowflakings of X which admit a bi-Lipschitz embedding into a Hilbert space.

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