Advances in Operator Theory

On some inequalities for the approximation numbers in Banach algebras

Nicolae Tiţa and Maria Talpău Dimitriu

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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

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

Received: 5 March 2018
Accepted: 19 April 2018
First available in Project Euclid: 10 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Banach algebra ideal approximation number


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.

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