Quantitative version of the BishopPhelpsBollobas theorem for operators with values in a space with the property $\beta$ 

Author 
vova1kadets@yahoo.com; mariiasoloviova93@gmail.com
School of Mathematics and Informatics;
Kharkiv V.N. Karazin National University, Kharkiv, Ukraine

Abstract 
The BishopPhelpsBollobas property for operators deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T\colon X\rightarrow Y$ nearly attains its norm by an operator $F$ and a vector $z$, respectively, such that $F$ attains its norm at $z$. We study the possible estimates from above and from below for parameters that measure the rate of approximation in the BishopPhelpsBollobas property for operators for the case of $Y$ having the property $\beta$ of Lindenstrauss.

Keywords 
BishopPhelpsBollobas theorem; normattaining operators; property $\beta$ of Lindenstrauss

DOI 
doi:10.15330/ms.47.1.7190

Reference 
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Pages 
7190

Volume 
47

Issue 
1

Year 
2017

Journal 
Matematychni Studii

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