A Bishop-Phelps-Bollobas theorem for disc algebra

2023/05/01 by Bala, Neeru, Sarkar, Jaydeb, Sensarma, Aryaman
#30H05 #46E15 #46E22 #46H10 #46J10 #47L20 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2305.00859

Abstract

Let \mathbbD represent the open unit disc in ℂ. Denote by A(\mathbbD) the disc algebra, and \mathscrB(X, A(\mathbb\mathbbD)) the Banach space of all bounded linear operators from a Banach space X into A(\mathbbD). We prove that, under the assumption of equicontinuity at a point in ∂ \mathbbD, the Bishop-Phelps-Bollobás property holds for \mathscrB(X, A(\mathbb\mathbbD)).

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