The principal investigator, David P. Blecher, is pursuing three main lines of research, focused around some of the most critical problems in `noncommutative linear analysis', and in particular in the new but seminal field of `operator spaces'. These lines are 1)the completely isometric theory of operator spaces, most particularly a continuing development of a useful `noncommutative Choquet theory', 2) the completely isomorphic theory of operator spaces, 3) the general theory of operator algebras. This project also includes an intensive focus on diverse applications of the above technology.
A major trend in mathematics in the 21st century, inspired largely by physics, is toward `noncommutative' or `quantized' phenomena. This thrust has permeated most branches of mathematics. In the vast area known as functional analysis, this trend has appeared notably under the name of `operator spaces'. The main purpose of the young but seminal field of operator spaces, is to provide new and appropriate tools to solve problems concerning spaces of operators on Hilbert space arising in `noncommutative mathematics'. With this project, the investigator (on his own, and together with several of the other major researchers in this area) is attacking several of the most important and critical problems in the subject. This work will provide major new tools, which will have applications to several diverse fields: linear analysis, operator theory, operator algebras, and quantum physics.
