Sums of idempotents in Banach algebras
- Authors: Mohubedu, Sethibe Titus
- Date: 2008-06-12T05:35:24Z
- Subjects: Banach algebras , Idempotents
- Type: Thesis
- Identifier: uj:2655 , http://hdl.handle.net/10210/609
- Description: Dr. D. Behrendt Prof. H. Raubenheimer
- Full Text:
- Authors: Mohubedu, Sethibe Titus
- Date: 2008-06-12T05:35:24Z
- Subjects: Banach algebras , Idempotents
- Type: Thesis
- Identifier: uj:2655 , http://hdl.handle.net/10210/609
- Description: Dr. D. Behrendt Prof. H. Raubenheimer
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Rank, trace and determinant in Banach algebras
- Authors: Schulz, Francois Petrus
- Date: 2015-04-23
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:13567 , http://hdl.handle.net/10210/13707
- Description: M.Sc. (Mathematics) , Determinants have been present since the very beginning of functional analysis. The determinants of in nite matrices were investigated for the rst time by the astronomer G. W. Hill in his studies on lunar theory. These ideas were then made exact by H. Poincare in 1886. Ten years later, H. von Koch polished and generalized Poincare's results. In 1903, I. Fredholm provided groundbreaking research into the development of a determinant theory for integral operators ...
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- Authors: Schulz, Francois Petrus
- Date: 2015-04-23
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:13567 , http://hdl.handle.net/10210/13707
- Description: M.Sc. (Mathematics) , Determinants have been present since the very beginning of functional analysis. The determinants of in nite matrices were investigated for the rst time by the astronomer G. W. Hill in his studies on lunar theory. These ideas were then made exact by H. Poincare in 1886. Ten years later, H. von Koch polished and generalized Poincare's results. In 1903, I. Fredholm provided groundbreaking research into the development of a determinant theory for integral operators ...
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On inessential elements in Banach algebras
- Authors: Behrendt, Darren Robin
- Date: 2012-01-24
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:1917 , http://hdl.handle.net/10210/4279
- Description: D.Phil.
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- Authors: Behrendt, Darren Robin
- Date: 2012-01-24
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:1917 , http://hdl.handle.net/10210/4279
- Description: D.Phil.
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Commuting exponentials in Banach algebras
- Authors: Lukoto, Tshikhudo
- Date: 2017
- Subjects: Banach algebras , Exponential functions
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/244031 , uj:25232
- Description: M.Sc. (Mathematics) , Abstract: Please refer to full text to view abstract
- Full Text:
- Authors: Lukoto, Tshikhudo
- Date: 2017
- Subjects: Banach algebras , Exponential functions
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/244031 , uj:25232
- Description: M.Sc. (Mathematics) , Abstract: Please refer to full text to view abstract
- Full Text:
Regularities in Banach algebras
- Authors: Weitz, Craig Stewart
- Date: 2010-05-25T06:08:38Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:6830 , http://hdl.handle.net/10210/3263
- Description: M.Sc.
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- Authors: Weitz, Craig Stewart
- Date: 2010-05-25T06:08:38Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:6830 , http://hdl.handle.net/10210/3263
- Description: M.Sc.
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Regularities and the index for Fredholm elements in a banach algebra via a trace
- Authors: Swartz, André Michael
- Date: 2016
- Subjects: Banach algebras , Fredholm equations , Fredholm operators
- Language: English
- Type: Doctoral (Thesis)
- Identifier: http://hdl.handle.net/10210/124820 , uj:20962
- Description: Abstract: Please refer to full text to view abstract , Ph.D. (Mathematics)
- Full Text:
- Authors: Swartz, André Michael
- Date: 2016
- Subjects: Banach algebras , Fredholm equations , Fredholm operators
- Language: English
- Type: Doctoral (Thesis)
- Identifier: http://hdl.handle.net/10210/124820 , uj:20962
- Description: Abstract: Please refer to full text to view abstract , Ph.D. (Mathematics)
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An analytic approach to the spectral characterization of the radical
- Authors: Bower, Hendri
- Date: 2016
- Subjects: Density functionals , Banach algebras , Spectral theory (Mathematics) , Proof theory , Zemanek, Jaroslav
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/124927 , uj:20975
- Description: Abstract: Please refer to full text to view abstract , M.Sc. (Mathematics)
- Full Text:
- Authors: Bower, Hendri
- Date: 2016
- Subjects: Density functionals , Banach algebras , Spectral theory (Mathematics) , Proof theory , Zemanek, Jaroslav
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/124927 , uj:20975
- Description: Abstract: Please refer to full text to view abstract , M.Sc. (Mathematics)
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Derivations mapping into the radical
- Authors: Ndipingwi, Christopher Mbuh
- Date: 2010-05-27T06:03:08Z
- Subjects: Banach algebras , Radical theory
- Type: Thesis
- Identifier: http://ujcontent.uj.ac.za8080/10210/379789 , uj:6842 , http://hdl.handle.net/10210/3274
- Description: M.Sc. , One of the earliest results (1955) in the theory of derivations is the celebrated theorem of I. M. Singer and J. Wermer [14] which asserts that every bounded derivation on a commutative Banach algebra has range contained in the radical. However, they immediately conjectured that their result will still hold if the boundedness condition was dropped. This conjecture of Singer and Wermer was confirmed only in 1988, by M. P. Thomas [23], when he showed that every derivation (bounded or unbounded) on a commutative Banach algebra has range contained in the radical. But it is not known whether an analogue of the Kleinecke-Shirokov Theorem holds for everywhere defined unbounded derivation.
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- Authors: Ndipingwi, Christopher Mbuh
- Date: 2010-05-27T06:03:08Z
- Subjects: Banach algebras , Radical theory
- Type: Thesis
- Identifier: http://ujcontent.uj.ac.za8080/10210/379789 , uj:6842 , http://hdl.handle.net/10210/3274
- Description: M.Sc. , One of the earliest results (1955) in the theory of derivations is the celebrated theorem of I. M. Singer and J. Wermer [14] which asserts that every bounded derivation on a commutative Banach algebra has range contained in the radical. However, they immediately conjectured that their result will still hold if the boundedness condition was dropped. This conjecture of Singer and Wermer was confirmed only in 1988, by M. P. Thomas [23], when he showed that every derivation (bounded or unbounded) on a commutative Banach algebra has range contained in the radical. But it is not known whether an analogue of the Kleinecke-Shirokov Theorem holds for everywhere defined unbounded derivation.
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Quasinilpotent equivalence in Banach algebras
- Authors: Kone, Namadzavho Bernard
- Date: 2009-03-30T14:08:07Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:8225 , http://hdl.handle.net/10210/2313
- Description: M.Sc.
- Full Text:
- Authors: Kone, Namadzavho Bernard
- Date: 2009-03-30T14:08:07Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:8225 , http://hdl.handle.net/10210/2313
- Description: M.Sc.
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Characterizations of scalars in Banach algebras
- Authors: Braatvedt, Gareth
- Date: 2011-06-22T10:42:40Z
- Subjects: Banach algebras , Scalar field theory
- Type: Thesis
- Identifier: uj:7110 , http://hdl.handle.net/10210/3704
- Description: D.Phil.
- Full Text:
- Authors: Braatvedt, Gareth
- Date: 2011-06-22T10:42:40Z
- Subjects: Banach algebras , Scalar field theory
- Type: Thesis
- Identifier: uj:7110 , http://hdl.handle.net/10210/3704
- Description: D.Phil.
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Riesz- en Fredholmteorie in Banach-algebras
- Authors: Vermaak, Jacobus Andries
- Date: 2014-09-11
- Subjects: Banach algebras , Banach spaces , Spectral theory (Mathematics) , Freeholm operators
- Type: Thesis
- Identifier: uj:12268 , http://hdl.handle.net/10210/12031
- Description: M.Sc. (Mathematics) , Please refer to full text to view abstract
- Full Text:
- Authors: Vermaak, Jacobus Andries
- Date: 2014-09-11
- Subjects: Banach algebras , Banach spaces , Spectral theory (Mathematics) , Freeholm operators
- Type: Thesis
- Identifier: uj:12268 , http://hdl.handle.net/10210/12031
- Description: M.Sc. (Mathematics) , Please refer to full text to view abstract
- Full Text:
Continuity of generalized inverses in Banach algebras
- Authors: Behrendt, Darren Robin
- Date: 2012-01-24
- Subjects: Banach algebras , Generalized inverses , Linear operators
- Type: Thesis
- Identifier: uj:1938 , http://hdl.handle.net/10210/4298
- Description: M.Sc.
- Full Text:
- Authors: Behrendt, Darren Robin
- Date: 2012-01-24
- Subjects: Banach algebras , Generalized inverses , Linear operators
- Type: Thesis
- Identifier: uj:1938 , http://hdl.handle.net/10210/4298
- Description: M.Sc.
- Full Text:
Uniqueness of the norm topology in Banach algebras
- Authors: Cawdery, John Alexander
- Date: 2012-06-07
- Subjects: Banach algebras , Topology
- Type: Thesis
- Identifier: uj:8733 , http://hdl.handle.net/10210/5083
- Description: M.Sc. , 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.
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- Authors: Cawdery, John Alexander
- Date: 2012-06-07
- Subjects: Banach algebras , Topology
- Type: Thesis
- Identifier: uj:8733 , http://hdl.handle.net/10210/5083
- Description: M.Sc. , 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.
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Quasi inessential elements in Banach algebras
- Authors: Burnard, Chantel
- Date: 2012-06-11
- Subjects: Banach algebras , Quasi inessential elements
- Type: Thesis
- Identifier: uj:8759 , http://hdl.handle.net/10210/5110
- Description: M.Sc.
- Full Text:
- Authors: Burnard, Chantel
- Date: 2012-06-11
- Subjects: Banach algebras , Quasi inessential elements
- Type: Thesis
- Identifier: uj:8759 , http://hdl.handle.net/10210/5110
- Description: M.Sc.
- Full Text:
On the role of subharmonic functions in the spectral theory of general Banach algebras
- Authors: Moolman, Ruan
- Date: 2010-02-23T08:13:24Z
- Subjects: Banach algebras , Spectral theory (Mathematics) , Algebraic functions
- Type: Thesis
- Identifier: uj:6625 , http://hdl.handle.net/10210/3026
- Description: M.Sc.
- Full Text:
- Authors: Moolman, Ruan
- Date: 2010-02-23T08:13:24Z
- Subjects: Banach algebras , Spectral theory (Mathematics) , Algebraic functions
- Type: Thesis
- Identifier: uj:6625 , http://hdl.handle.net/10210/3026
- Description: M.Sc.
- Full Text:
On approximate identities and topological divisors of zero in Banach algebras
- Authors: Hasse, Melanie Alexandra
- Date: 2016
- Subjects: Banach algebras , Spectral theory (Mathematics) , Tensor products , Topological algebras
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/244008 , uj:25229
- Description: M.Sc. , Abstract: Please refer to full text to view abstract
- Full Text:
- Authors: Hasse, Melanie Alexandra
- Date: 2016
- Subjects: Banach algebras , Spectral theory (Mathematics) , Tensor products , Topological algebras
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/244008 , uj:25229
- Description: M.Sc. , Abstract: Please refer to full text to view abstract
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Rank in Banach algebras
- Authors: Renison, Martin
- Date: 2008-06-27T13:46:45Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:10084 , http://hdl.handle.net/10210/746
- Description: Dr. R.M Brits
- Full Text:
- Authors: Renison, Martin
- Date: 2008-06-27T13:46:45Z
- Subjects: Banach algebras
- Type: Thesis
- Identifier: uj:10084 , http://hdl.handle.net/10210/746
- Description: Dr. R.M Brits
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Multiplicatively spectrum preserving functions on Banach algebras
- Authors: Touré, Cheick Kader
- Date: 2019
- Subjects: Banach algebras , Algebras, Linear
- Language: English
- Type: Doctoral (Thesis)
- Identifier: http://hdl.handle.net/10210/418856 , uj:35530
- Description: Abstract: Please refer to full text to view abstract. , Ph.D. (Pure and Applied Mathematics)
- Full Text:
- Authors: Touré, Cheick Kader
- Date: 2019
- Subjects: Banach algebras , Algebras, Linear
- Language: English
- Type: Doctoral (Thesis)
- Identifier: http://hdl.handle.net/10210/418856 , uj:35530
- Description: Abstract: Please refer to full text to view abstract. , Ph.D. (Pure and Applied Mathematics)
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Applications of algebraic topology to spectral theory in Banach algebras
- Authors: Askes, Miles
- Date: 2019
- Subjects: Banach algebras , Algebras, Linear
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/416473 , uj:35231
- Description: Abstract: Please refer to full text to view abstract. , M.Sc. (Applied Mathematics)
- Full Text:
- Authors: Askes, Miles
- Date: 2019
- Subjects: Banach algebras , Algebras, Linear
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/416473 , uj:35231
- Description: Abstract: Please refer to full text to view abstract. , M.Sc. (Applied Mathematics)
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