New norm and numerical radius bounds via advanced Cauchy-Schwarz inequalities

In the present paper, the authors establish new inner product inequalities of Cauchy-Schwarz type, in which expressions involving multiple operators (typically sums such as A + B) are controlled within a single inequality (so-called mixed Cauchy-Schwarz inequalities). These refinements are then used to derive bounds for operator expressions involving unitarily invariant norms and the numerical radius