On the Bishop-Phelps-Bollobas property for numerical radius in C(K)-spaces
Antonio Avil\'es, Antonio J. Guirao, Jos\'e Rodr\'iguez
TL;DR
This paper investigates the Bishop-Phelps-Bollobas property for numerical radius in C(K) spaces, identifying conditions like metrizability of K that guarantee this property holds.
Contribution
The paper provides new sufficient conditions, including metrizability, under which C(K) spaces exhibit the Bishop-Phelps-Bollobas property for numerical radius.
Findings
C(K) has the property when K is metrizable
Several sufficient conditions for the property are established
The property is characterized within the framework of C(K) spaces
Abstract
We study the Bishop-Phelps-Bollobas property for numerical radius within the framework of C(K) spaces. We present several sufficient conditions on a compact space K ensuring that C(K) has the Bishop-Phelps-Bollobas property for numerical radius. In particular, we show that C(K) has such property whenever K is metrizable.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Optimization and Variational Analysis