Seminar by Dr. Samya Kumar Ray, IISERTVM on 2 September 2025

We are very glad to announce the talk by Dr. Samya Kumar Ray, Assistant Professor, IISER TVM, in our seminar series.

Speaker: Dr. Samya Kumar Ray
Title of the talk: Operator spaces
Broad area of research: Functional Analysis
Date: 02/09/2025
Time: 4 pm
Venue: MSB 410

Abstract: Operator spaces, also known as “quantized Banach spaces,” provide the natural framework for studying noncommutative functional analysis. Unlike classical Banach spaces, operator spaces carry a matrix norm structure that reflects their realization as concrete subspaces of bounded operators on a Hilbert space. This enriched structure allows one to extend classical Banach space theory to the realm of operator algebras, where completely bounded maps replace bounded linear maps.

In this talk, I will introduce the fundamental ideas of operator space theory: Ruan’s axioms, concrete realizations, and the role of completely bounded maps. I will discuss basic constructions such as the operator space projective and injective tensor products, and highlight how these tools connect to C^*-algebras, noncommutative L_p-spaces, and quantum probability. Time permitting, I will also touch upon applications to dilation theory and noncommutative harmonic analysis.

The lecture is aimed at a broad mathematical audience with some background in functional analysis or operator algebras. No prior knowledge of operator space theory will be assumed.