Uniqueness of the norm topology in Banach algebras

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dc.contributor.advisor Dr. R.M. Brits en_US
dc.contributor.author Cawdery, John Alexander
dc.date.accessioned 2012-06-07T13:32:56Z
dc.date.available 2012-06-07T13:32:56Z
dc.date.issued 2012-06-07
dc.date.submitted 2011-10-04
dc.identifier.uri http://hdl.handle.net/10210/5083
dc.description M.Sc. en_US
dc.description.abstract The aim of this dissertation will be an investigation into a classical result which asserts the uniqueness of the norm topology on a semi-simple Banach algebra. For a commutative semi-simple Banach algebra, say A, it is relatively simple matter, with the aid of the Closed Graph Theorem, to show that all Banach algebra norms on A must be equivalent. The same result for non-commutative Banach algebras was conjectured by I. Kaplansky in the 1950’s and solved more then a decade later, in 1967, by B E Johnson. However, Johnson’s proof was difficult and relied heavily on representation theory. As a result, the problem remained unsolved for the more difficult situation of Jordan Banach algebras. Fifteen years later in 1982, B. Aupetit succeeded in proving Johnson’s result, using a subharmonic method that was independent of algebra representations. Moreover he could, using these techniques, also settle the problem in the Jordan Banach algebra case. A while later, in 1989, T. Ransford provided a shorter algebraic proof of Johnson’s result using the well-known spectral radius formula. This dissertation will be a comparative study of the three different approaches on the problem for Banach algebras. en_US
dc.language.iso en en_US
dc.subject Banach algebras en_US
dc.subject Topology en_US
dc.title Uniqueness of the norm topology in Banach algebras en_US
dc.type Thesis en_US

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