Soloviova M. Approximation by norm attaining functional and operators

The PhD thesis deals with approximation of linear continuous functionals and operators by norm attaining one. The Bishop-Phelps-Bollobas theorem allows to approximate at the same time a functional and a vector in which it almost attains the norm. We relate the modulus of uniform non-squareness with the Bishop-Phelps-Bollobás modulus. Also we introduce two concepts of norm attainment for Lipschitz functionals and study their properties. Besides we study the Bishop-Phelps-Bollobas property for operators. We extend the already known results about the Bishop-Phelps-Bollobas property for Asplund operators to a wider class of Banach spaces. We introduce the Bishop-Phelps-Bollobas moduli for operators and study the possible estimates from above and from below.