Document Type Master's Dissertation Author Lee, Wha-Suck URN etd-01182005-113356 Document Title Ideal perturbation of elements in C ^{*}-algebrasDegree 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 AbstractThe aim of this thesis is to prove the lifting property of zero divisors, n-zerodivisors, nilpotent elements and a criteria for the lifting of polynomially ideal

elements in C

^{*}-algebras. Chapter 1 establishes the foundation on which themachinery to prove the lifting properties stated above rests upon. Chapter

2 proves the lifting of zero divisors in C

^{*}-algebras. The generalization of thisproblem to lifting n-zero divisors in C

^{*}-algebras requires the advent of the coronaC

^{*}-algebra, a result of the school of non-commutative topology. The actualproof 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 elementalso 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 liftingof 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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