In this paper, we generalize some inequalities for the approximation numbers of an element in a normed (Banach) algebra $X$ and, as an application, we present inequalities for the quasinorms of some ideals defined by means of the approximation numbers.
In particular, if $X=L(E)$ - the algebra of linear and bounded operators $T:E \to E$, where $E$ is a Banach space, we obtain inequalities for certain quasinorms of operators.
"On some inequalities for the approximation numbers in Banach algebras." Adv. Oper. Theory 4 (1) 156 - 163, Winter 2019. https://doi.org/10.15352/aot.1802-1314