{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4ZKLNXILH7YL7GSWRHGJVZMVVC","short_pith_number":"pith:4ZKLNXIL","schema_version":"1.0","canonical_sha256":"e654b6dd0b3ff0bf9a5689cc9ae595a8a274e30a3fc049cb09acb16e0943737a","source":{"kind":"arxiv","id":"1406.0445","version":3},"attestation_state":"computed","paper":{"title":"Approximation numbers of composition operators on $H^p$ spaces of Dirichlet series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Fr\\'ed\\'eric Bayart, Herv\\'e Queff\\'elec, Kristian Seip","submitted_at":"2014-06-02T17:06:44Z","abstract_excerpt":"By a theorem of Bayart, $\\varphi$ generates a bounded composition operator on the Hardy space $\\Hp$of Dirichlet series ($1\\le p<\\infty$) only if $\\varphi(s)=c_0 s+\\psi(s)$, where $c_0$ is a nonnegative integer and $\\psi$ a Dirichlet series with the following mapping properties: $\\psi$ maps the right half-plane into the half-plane $\\Real s >1/2$ if $c_0=0$ and is either identically zero or maps the right half-plane into itself if $c_0$ is positive. It is shown that the $n$th approximation numbers of bounded composition operators on $\\Hp$ are bounded below by a constant times $r^n$ for some $01/2$ if $c_0=0$ and is either identically zero or maps the right half-plane into itself if $c_0$ is positive. It is shown that the $n$th approximation numbers of bounded composition operators on $\\Hp$ are bounded below by a constant times $r^n$ for some $0