Document Type: Special issue: Trends in Operators on Banach Spaces
Transilvania University of Brașov, Romania
Department of Mathematics and Informatics, Transilvania University of Braşov, Romania
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.