### On some inequalities for the approximation numbers in Banach algebras

#### 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.

#### Article information

Source
Adv. Oper. Theory, Volume 4, Number 1 (2019), 156-163.

Dates
Accepted: 19 April 2018
First available in Project Euclid: 10 May 2018

https://projecteuclid.org/euclid.aot/1525917620

Digital Object Identifier
doi:10.15352/aot.1802-1314

Mathematical Reviews number (MathSciNet)
MR3867339

Zentralblatt MATH identifier
06946448

Subjects
Primary: 47A63: Operator inequalities
Secondary: 47A58: Operator approximation theory 46H10: Ideals and subalgebras

#### Citation

Tiţa, Nicolae; Talpău Dimitriu, Maria. On some inequalities for the approximation numbers in Banach algebras. Adv. Oper. Theory 4 (2019), no. 1, 156--163. doi:10.15352/aot.1802-1314. https://projecteuclid.org/euclid.aot/1525917620

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