Some results in non-multiplicative \(B^ q\)-theory
While the closed subspace \(B^ q\) of the q-almost-even number- theoretical functions \((1<q<\infty)\) does show uniform convexity, the Banach space \(b^ q\), sequence space of Besicovitch, does not. Proving and confirming by different methods from functional analysis two special theorems of the non-multiplicative \(B^ q\)-theory has been the particular goal of investigation. This leads us to present necessary and sufficient criteria for well-founded final conclusion as to when \(B^ 1\)-functions are \(B^ q\)-functions as well.
q-almost-even number-theoretical functions
scientific article; zbMATH DE number 4087767