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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