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Kim, Sun Kwang; Lee, Han Ju; Martín, Miguel

On the Bishop-Phelps-Bollobás property for numerical radius. (English) Zbl 1473.46011

Abstr. Appl. Anal. 2014, Article ID 479208, 15 p. (2014).
Summary: We study the Bishop-Phelps-Bollobás property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu. Among other results, we show that \(L_1 \left(\mu\right)\)-spaces have this property for every measure \(\mu\). On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu. In particular, this shows that the Radon-Nikodým property (even reflexivity) is not enough to get BPBp-nu.

Cited in 1 Review
Cited in 6 Documents

MSC:

46B04 Isometric theory of Banach spaces
47A12 Numerical range, numerical radius

Keywords:

Bishop-Phelps-Bollobás property; numerical radius
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\textit{S. K. Kim} et al., Abstr. Appl. Anal. 2014, Article ID 479208, 15 p. (2014; Zbl 1473.46011)
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References:

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