Analysis Seminar Time: 02:40 PM -- 03:30 PM Host: Sourav Pal Speaker: Saikat Roy Title: Applications of Birkhoff-James orthogonality and its connection with dilation Abstract: Birkhoff-James orthogonality is a generalized notion of orthogonality that extends the inner product orthogonality to the setting of Banach spaces. In this talk, we present some of its applications in geometry of Banach spaces and its relation with norming properties of some subspaces of Banach space. We also consider operator orthogonality and its connection with the unitary and isometric dilations. We study the case when unitary (isometric) dilations of two contractions preserve the orthogonality relation between the basic contractions.