Phiri, Isaac (2016) Spectrum-Preserving Maps on Banach Algebras. Masters thesis, University of Zambia.
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Abstract
The classical Gleason-Kahane-Z˙ elazko’s Theorem gave rise to the so-called Kaplansky’s problem. This theorem states that a linear functional on a complex Banach algebra A is multiplicative (and non-zero) if and only if (a) 2 sp(a) (a 2 A), where sp(a) denotes the spectrum of a. The so-called Kaplansky’s problem is concerned with identifying the Jordan homomorphisms among all linear maps : A ! B between complex Banach algebras A and B in terms of spectra. To this end Kaplansky suggested to translate (a) 2 sp(a) (a 2 A) such that is a linear functional for a linear map : A ! B into the property of shrinking the spectrum, that is sp
| Item Type: | Thesis (Masters) |
|---|---|
| Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
| Divisions: | Africana |
| Depositing User: | Geoffrey Obatsa |
| Date Deposited: | 28 Aug 2018 12:57 |
| Last Modified: | 28 Aug 2018 12:57 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/8468 |
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