Title page for ETD etd-01182005-113356


Document Type Master's Dissertation
Author Lee, Wha-Suck
URN etd-01182005-113356
Document Title Ideal perturbation of elements in C*-algebras
Degree MSc (Mathematics and Applied Mathematics)
Department Mathematics and Applied Mathematics
Supervisor
Advisor Name Title
Prof A Ströh
Keywords
  • no key words available
Date 2005-06-14
Availability unrestricted
Abstract
The aim of this thesis is to prove the lifting property of zero divisors, n-zero

divisors, nilpotent elements and a criteria for the lifting of polynomially ideal

elements in C*-algebras. Chapter 1 establishes the foundation on which the

machinery to prove the lifting properties stated above rests upon. Chapter

2 proves the lifting of zero divisors in C*-algebras. The generalization of this

problem to lifting n-zero divisors in C*-algebras requires the advent of the corona

C*-algebra, a result of the school of non-commutative topology. The actual

proof reduces the general case to the case of the corona of a non-unital _-unital

C*-algebra. Chapter 3 proves the lifting of the property of a nilpotent element

also by a reduction to the case of the corona of a non-unital _-unital C*-algebra.

The case of the corona of a non-unital _-unital C*-algebra is proved via a lifting

of a triangular form in the corona. Finally in Chapter 4, a criterion is established

to determine exactly when the property of a polynomially ideal element can be

lifted. It is also shown that due to topological obstructions, this is not true in

any C*-algebra.

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