Functional Analysis: Quasinilpotent Equivalence in Banach Algebras

In preliminaries, Chapter 2, we define a Banach Algebra, Spectrum, Resolvent Set, Spectral Radius, Homomorphism, Antihormomophism, Nilpotent and Quasinilpotent. Propositions with proofs are used to explain the concept of Quasinilpotent Equivalence and the book culminates in showing when Quasinilpotent implies equality by proving the theorem: Suppose that a and b in a Banach Algebra A are quasinilpotent equivalent and suppose that there is an entire function f which has simple zeros. If f(a) = f(b) = 0, then a = b.

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Namadzavho B Kone passed matric at Mbilwi High School and a Secondary Teachers Diploma thereafter. He worked as a high school Maths and Science teacher for 10 years and studied for a degree majoring in Maths part time. He joined an NGO that trained Maths teachers before being appointed a Maths Lecturer and obtained a Masters degree in Maths.