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arXiv · 2305.00859

A Bishop-Phelps-Bollobas theorem for disc algebra

Neeru Bala·Jaydeb Sarkar·Aryaman Sensarma
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Abstract

Let $\mathbb{D}$ represent the open unit disc in $\mathbb{C}$. Denote by $A(\mathbb{D})$ the disc algebra, and $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$ the Banach space of all bounded linear operators from a Banach space $X$ into $A(\mathbb{D})$. We prove that, under the assumption of equicontinuity at a point in $\partial \mathbb{D}$, the Bishop-Phelps-Bollob\'{a}s property holds for $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$.

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Neeru Bala, Jaydeb Sarkar, Aryaman Sensarma. 2023-05-01. A Bishop-Phelps-Bollobas theorem for disc algebra. https://arxiv.org/abs/2305.00859

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