Corresponding Banach spaces on time scales
Let \({\mathbb T}\) be a time scale, i.e. a nonempty closed subset of \({\mathbb R}\). The authors prove that for a given vector space \((\tilde V,+,\cdot)\) of functions \(f:{\mathbb T}\to{\mathbb R}\) and for the corresponding vector space \((V,\oplus,\odot)\) of positively regressive functions \(p\) (i.e., \(1+\mu(x)p(x)>0\) on \({\mathbb T}\) with the operations \(\oplus\) and \(\odot\) defined in ``usual'' time scales way), the cylinder transform \(\xi_\mu:(V,\oplus,\odot)\to(\tilde V,+,\cdot)\) is an isomorphism. This result is then extended to the Banach and Hilbert spaces setting.
scientific article; zbMATH DE number 2173202