Colloquium

Speaker: Taduri Srinivasa Siva Rama Krishnarao (Indian Statistical
Institute, Bangalore Centre, and University of Memphis)

Title: Proximinality for sums of closed subspaces

Abstract: In this talk we deal with the question of approximating minimizing sequences by sequence of proximinal vectors, for sums of closed subspaces. Motivated by some results of M. Feder and Pei-Kee Lin, we show that for a finite dimensional sub-space F  and a strongly proximinal subspace Y  of a Banach space X , F  + Y  is a strongly proximinal subspace of X . We also show the universality of the difficulty involved for sums of subspaces by showing that for any
infinite dimensional Banach space X  there exists an infinite dimensional space Z  containing an isometric copy of X  as a strongly proximinal subspace and a strongly proximinal subspace W  of Z  such that the sum X  +W  is a closed, proximinal subspace of Z  that is not strongly proximinal in Z .

Bio: Professor Taduri is currently Fulbright-Nehru Academic and Professional Excellence Scholar at the Department of Mathematical scienced, University of Memphis. A senior professor from the Indian Statistical Institute, a Fellow of the Indian Academy of Sciences, he is the current Head of the Indian Statistical Institute, Bangalore centre.