Corpus ID: 237581574

A Bishop-Phelps-Bollob\'{a}s theorem for bounded analytic functions

  title={A Bishop-Phelps-Bollob\'\{a\}s theorem for bounded analytic functions},
  author={Neeru Bala and Kousik Dhara and Jaydeb Sarkar and Aryaman Sensarma},
Let H∞ denote the Banach algebra of all bounded analytic functions on the open unit disc and denote by B(H∞) the Banach space of all bounded linear operators from H ∞ to itself. We prove that the Bishop-Phelps-Bollobás property holds for B(H∞). As an application to our approach, we prove that the Bishop-Phelps-Bollobás property also holds for operator ideals of B(H∞). 


The Bishop-Phelps-Bollobás theorem for operators
We prove the Bishop–Phelps–Bollobas theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize thoseExpand
A Urysohn-type theorem and the Bishop-Phelps-Bollobás theorem for holomorphic functions
Abstract A Urysohn-type theorem is introduced for a subalgebra of the algebra C b ( Ω ) of all bounded complex-valued continuous functions on a Hausdorff topological space Ω. With use of thisExpand
A counterexample to the Bishop-Phelps Theorem in complex spaces
The Bishop-Phelps Theorem asserts that the set of functionals which attain the maximum value on a closed bounded convex subsetS of a real Banach spaceX is norm dense inX*. We show that this statementExpand
A Bishop–Phelps–Bollobás type theorem for uniform algebras
Abstract This paper is devoted to showing that Asplund operators with range in a uniform Banach algebra have the Bishop–Phelps–Bollobas property, i.e., they are approximated by norm attaining AsplundExpand
The Bishop-Phelps-Bollobás theorem and Asplund operators
This paper deals with a strengthening of the Bishop-Phelps property for operators that in the literature is called the Bishop-Phelps-Bollobás property. Let X be a Banach space and L a locally compactExpand
Non-Asplund Banach spaces and operators
Let W and Z be Banach spaces such that Z is separable and let R:W⟶Z R : W ⟶ Z be a (continuous, linear) operator. We study consequences of the adjoint operator R ⁎ R ⁎ having non-separable range.Expand
Denseness of norm attaining mappings
The Bishop-Phelps Theorem states that the set of (bounded and linear) functionals on a Banach space that attain their norms is dense in the dual. In the complex case, Lomonosov proved that there mayExpand
Banach spaces of analytic functions
In this paper, we explore certain Banach spaces of analytic functions. In particular, we study the space A -I, demonstrating some of its basic properties including non-separability. We ask theExpand
The Bishop-Phelps-Bollobás version of Lindenstrauss properties A and B
We study a Bishop-Phelps-Bollob\'as version of Lindenstrauss properties A and B. For domain spaces, we study Banach spaces $X$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\'as property (BPBp) forExpand
On holomorphic functions attaining their norms
Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that XExpand