On the compact operators case of the Bishop-Phelps-Bollobás property for numerical radius

2021/02/22 by Garcia, Domingo, Maestre, Manuel, Martin, Miguel +1
#46B25 #46B28 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46B04 #Secondary: 46B20

paper · doi:10.48550/arxiv.2102.10937

Abstract

We study the Bishop-Phelps-Bollobás property for numerical radius restricted to the case of compact operators (BPBp-nu for compact operators in short). We show that C₀(L) spaces have the BPBp-nu for compact operators for every Hausdorff topological locally compact space L. To this end, on the one hand, we provide some techniques allowing to pass the BPBp-nu for compact operators from subspaces to the whole space and, on the other hand, we prove some strong approximation property of C₀(L) spaces and their duals. Besides, we also show that real Hilbert spaces and isometric preduals of ℓ₁ have the BPBp-nu for compact operators.

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