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Title: Convex combinations of unitaries in JB*-algebras
Author: Siddiqui, Akhlag Ahmad
Awarding Body: Heriot-Watt University
Current Institution: Heriot-Watt University
Date of Award: 1996
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In this thesis we investigate results about convex combinations of unitaries in unital J B* -algebras, the Jordan algebra analogues of C* -algebras. After giving background material in chapter 1 we introduce the concept of unitary isotopes of J B* -algebras in chapter 2 and develop their theory including identification of their centre. We also show important unit aries for our results come from the polar decomposition of invertible elements. In chapter 3 we investigate which elements are self-adjoint in some isotope to start the development of the theory of convex combinations of two or more unitaries. This leads us in chapter 4 to introduce and give examples of a subclass of J B* -algebras in which the invertible elements are dense. We also show that extreme points of the unit ball sufficiently close to the invertibles must be unit aries and deduce that in the subclass, all extreme points are unitaries. In chapter 5 we look the relationships between the distance of an element to the invertibles or unit aries and special types of convex combinations, for example those of unit aries having all (but one) of the coefficients equal and those of unit ball elements only one of which need be unitary. Finally in chapter 6 we investigate some possible further developments and open problems
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Pure mathematics Mathematics