|Samya Kumar Ray
|Indian Statistical Institute, Kolkata
One of the most important questions in Banach space geometry is when does a Banach space embed into another Banach space isometrically or almost isometrically. In this talk, we discuss some results regarding existence of isometric embeddings of S^m_q into S^n_p where S^n_p is the usual Schatten-p class over n × n complex matrices. We also present some results when p and q are also allowed to be less than 1. We will explain several new ingredients related to perturbation theory of linear operators, namely Kato-Rellich theorem, theory of multiple operator integrals, norm-parallelism and Birkhoff-James orthogonality, followed by thorough and careful case by case analysis, which are essential to our work. This talk is based on work done in collaboration with Arup Chattopadhya, Guixiang Hong, Avijit Pal and Chandan Pradhan.