Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589923 | Journal of Functional Analysis | 2015 | 37 Pages |
By a theorem of Gordon and Hedenmalm, φ generates a bounded composition operator on the Hilbert space H2H2 of Dirichlet series ∑nbnn−s∑nbnn−s with square-summable coefficients bnbn if and only if φ(s)=c0s+ψ(s)φ(s)=c0s+ψ(s), where c0c0 is a nonnegative integer and ψ a Dirichlet series with the following mapping properties: ψ maps the right half-plane into the half-plane Res>1/2 if c0=0c0=0 and is either identically zero or maps the right half-plane into itself if c0c0 is positive. It is shown that the n th approximation numbers of bounded composition operators on H2H2 are bounded below by a constant times rnrn for some 0