Hölder-Type Inequalities for Power Series of Operators in Hilbert Spaces - Najla Altwaijry; Silvestru Sever Dragomir; Kais Feki (Axioms, 2024)
Consider the power series with complex coefficients <semantics>h(z)=<msubsup>∑k=0∞</msubsup>akzk</semantics> and its modified version <semantics>ha(z)=<msubsup>∑k=0∞</msubsup>|ak|zk</semantics>. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of <semantics>h(z)</semantics> on the open disk <semantics>D(0,ρ)</semantics>, where <semantics>ρ</semantics> denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.