Arveson's Extension Theorem

Sutradhar, Arindam (2015) Arveson's Extension Theorem. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS dissertation of Arindam Sutradhar (10MS50)) Arindma_Sutradhar_10MS50.pdf - Submitted Version Restricted to Repository staff only Download (377kB)

Abstract

This thesis deals with the properties of positive maps and completely positive maps. The goal of the thesis is to proof Arveson's Extension Theorem and all the Chapters construct the tools that is needed to prove the theorem. In Chapter 1 we state the basics of C*-algebra and properties of positive elements. In Chapter 2 we define positive maps on operator system. In Chapter 3 we study the completely positive maps between C*-algebras. Chapter 4 consists of Stinespring Dilation Theorem which is a characterization of all completely positive maps. In Chapter 5 we study the maps from operatr system to Mn. In Chapter 6 we replace this Mn with B(H). Our final goal is to examine whether completely positive maps from operator system to B(H) can be extended to C*-algebra to B(H) completely positively which Arveson's Extension theorem deals with.

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