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• W2752067378 abstract "We study approximations of operators that nearly attain their norms in a given point by operators that attains their norm at the same point. When for operators between given Banach spaces $X$ and $Y$ such approximations exist, then we say that the pair $(X, Y)$ has the Bishop-Phelps-Bollob'as point property (BPBpp for short). In this paper we mostly concentrate on those $X$, called universal BPBpp domain spaces, such that $(X, Y)$ possesses BPBpp for every $Y$, and on those $Y$, called universal BPBpp range spaces, such that $(X, Y)$ enjoys BPBpp for every uniformly smooth $X$. We show that every universal BPBpp domain space is uniformly convex and that $L_p(mu)$ spaces fails to have this property when $p>2$. For universal BPBpp range space, we show that $L_p(mu)$ spaces fails it for $pgeq 2$. We also discuss a version of the BPBpp for compact operators. Finally, we demonstrate that a similar property, where a point at which operator nearly attains its norm can be approximated by a point at which the same operator attains its norm exactly, may happen only if one of the spaces $X$ and $Y$ in question is one-dimensional." @default.
• W2752067378 created "2017-09-15" @default.
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• W2752067378 date "2017-08-31" @default.
• W2752067378 modified "2023-09-23" @default.
• W2752067378 title "On the Bishop-Phelps-Bollob'as point property for operators" @default.
• W2752067378 hasPublicationYear "2017" @default.
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