Operator Algebras, Interpolation and Frames

University Of Houston, Houston TX

Investigators

Abstract

Abstract Paulsen My research will focus in three directions. I will continue to study injective envelopes, seeking deeper results about their structure and further applications of these objects to the study of operator spaces and C*-algebras. I will especially focus on attempting to develop a deeper understanding of the connections between injective envelopes and the weak expectation property. I will also continue to study applications of operator algebra techniques to the study of Nevanlinna-Pick type interpolation, especially focusing on the use of the C*-envelope and Schur ideals. The third direction that I will focus is the study of finite dimensional frames from the viewpoint of coding theory, especially the problem of determining optimal frames for certain coding theory problems.- My research on frames could have the broadest impact. Frames are used as a way to ensure accurate communication of analogue information in the presence of uncertainty, usually coming from a noisy communication channel. My work on frames from a coding theory point of view intends to find the optimal frames to use for transmitting data, when it is anticipated that some of the data will be lost during the transmission. My work is especially relevant to the problem of "lost packages". Here one assumes that the data is packaged into discrete "bundles" that are then transmitted separately, perhaps even over different channels, and then reassembled later. The problem is what to do if only some of the bundles arrive? Clearly, one wants to build some redundancy into the transmitted data so that one can still reassemble a message, that if not exactly the original message, is close to the original message in some sense.