On some inequalities for the approximation numbers in Banach Algebras

Document Type: Special issue: Trends in Operators on Banach Spaces

Authors

1 Transilvania University of Brașov, Romania

2 Department of Mathematics and Informatics, Transilvania University of Braşov, Romania

Abstract

‎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.

Keywords