Quantitative version of the Bishop-Phelps-Bollob\'as theorem for operators with values in a space with the property β
Abstract
The Bishop-Phelps-Bollob\'as property for operators deals with simultaneous approximation of an operator T and a vector x at which T: X→ 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-Bollob\'as property for operators for the case of Y having the property β of Lindenstrauss.
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