A Bishop-Phelps-Bollobás theorem for bounded analytic functions

2021/09/21 by Bala, Neeru, Dhara, Kousik, Sarkar, Jaydeb +1
#30H05 #46B20 #46B22 #46J10 #46J15 #47L20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2109.10125

Abstract

Let H^∞ denote the Banach algebra of all bounded analytic functions on the open unit disc and denote by \mathscrB(H^∞) the Banach space of all bounded linear operators from H^∞ to itself. We prove that the Bishop-Phelps-Bollobás property holds for \mathscrB(H^∞). As an application to our approach, we prove that the Bishop-Phelps-Bollobás property also holds for operator ideals of \mathscrB(H^∞).

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