A Bishop-Phelps-Bollobas theorem for disc algebra

Neeru Bala; Jaydeb Sarkar; Aryaman Sensarma

A Bishop-Phelps-Bollobas theorem for disc algebra

Functional Analysis 2023-05-02 v1 Complex Variables Operator Algebras

Authors: Neeru Bala , Jaydeb Sarkar , Aryaman Sensarma

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 $\mathscr{B}(X, A(\mathbb{\mathbb{D}}))$ .

Keywords

banach space properties banach algebras banach spaces

Cite

@article{arxiv.2305.00859,
  title  = {A Bishop-Phelps-Bollobas theorem for disc algebra},
  author = {Neeru Bala and Jaydeb Sarkar and Aryaman Sensarma},
  journal= {arXiv preprint arXiv:2305.00859},
  year   = {2023}
}

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12 pages

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