# Daugavet centers are separably determined

**Journal**: Matematychni Studii (Vol.40, No. 1)

**Publication Date**: 2013-07-01

**Authors** : Ivashyna T.;

**Page** : 66-70

**Keywords** : Daugavet center; Daugavet property; narrow operator;

### Abstract

A linear bounded operator $G$ acting from a Banach space $X$ into a Banach space $Y$ is a Daugavet center if every linear bounded rank-$1$ operator $Tcolon X to Y$ fulfills $|G+T|=|G|+|T|$. We prove that $G colon X to Y$ is a~Daugavet center if and only if for every separable subspaces $X_1subset X$ and $Y_1subset Y$ there exist separable subspaces $X_2subset X$ and $Y_2subset Y$ such that $X_1subset X_2$, $Y_1subset Y_2$, $G(X_2)subset Y_2$ and the restriction $G|_{X_2} colon X_2 to Y_2$ of $G$ is a Daugavet center. We apply this fact to study the set of $G$-narrow operators.

Other Latest Articles

- On growth order of solutions of differential equations in a neighborhood of a branch point
- Asymptotics of eigenvalues and eigenfunctions of energy-dependent Sturm-Liouville equations
- Differential equations and integral characterizations of timelike and spacelike spherical curves in the Minkowski space-time $E_1^4 $
- On a lower continuity of upper continuous mappings with values in the Sorgenfrey line(in Ukrainian)
- On a theorem of John and its generalizations

Last modified: 2014-01-13 20:10:12