Weakening of a local Bollobás type property and geometry of Banach spaces (Q6548060)

In this paper, the author characterizes the property weak \(L_{o,o}\) in terms of convergence of approximate norm attainment sets and proves that a pair of Banach spaces \((X,Y)\) satisfies the property weak \(L_{o,o}\) for compact operators if and only if \(X\) is reflexive. The author also investigates the property weak \(L_{o,o}\) for bilinear maps and obtains a connection of it with the property weak \(L_{o,o}\) for operators and characterizes some geometric properties of Banach spaces with the help of convergence of approximate norm attainment sets.