Quantitative version of the Bishop-Phelps-Bollobas theorem for operators with values in a space with the property $\beta$ |
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| Author |
vova1kadets@yahoo.com; mariiasoloviova93@gmail.com
School of Mathematics and Informatics;
Kharkiv V.N. Karazin National University, Kharkiv, Ukraine
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| Abstract |
The Bishop-Phelps-Bollobas 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 Bishop-Phelps-Bollobas property for operators for the case of $Y$ having the property $\beta$ of Lindenstrauss.
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| Keywords |
Bishop-Phelps-Bollobas theorem; norm-attaining operators; property $\beta$ of Lindenstrauss
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| DOI |
doi:10.15330/ms.47.1.71-90
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| Reference |
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| Pages |
71-90
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| Volume |
47
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| Issue |
1
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| Year |
2017
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| Journal |
Matematychni Studii
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| Full text of paper | |
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