| CODE | MAT5313 | ||||||||
| TITLE | C* - Algebras: General Theory | ||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||
| MQF LEVEL | 7 | ||||||||
| ECTS CREDITS | 15 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Basic Properties of Topological Vector Spaces and Locally Convex Spaces; Weak Topologies; Extreme Points and Kreine-Milman Theorem; Basic Properties of Banach Algebras; Basic Properties of C*-Algebras; Spectral Theory; Concrete C*-Algebras; Commutative C*-Algebras; Function Calculus; Order Structure; Positive Linear Functionals and Representations; Pure States and Irreducible Representations. Study-unit Aims: To further student's knowledge in the area of Functional Analysis, particularly Banach Algebras and C*-Algebras. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Analyse the algebraic and topological structure of C*-algebras; - Describe the spectral theory for operators; - Prove the Gelfand-Naimark-Segal representation theorem for C*-algebras; - Solve particular problems related to the subject of Operator Algebras. 2. Skills: By the end of the study-unit the student will be able to: - Formulate and investigate original problems in the field; - Apply methods and ideas covered in the study-unit to obtain new results; - Write mathematical material confidently, accurately and efficiently, in the area of Operator Algebras. Main Text/s and any supplementary readings: - J. Dixmier: C*-Algebras, North Holland, (1977). - R. V. Kadison and J. R. Ringrose: Fundamentals of the Theory of Operator Algebras, Academic Press (1986). - G.J. Murphy : C*-Algebras and Operator Theory, Academic Press (1990). - G. K. Pederson : C*-Algebras and their Automorphism groups, Academic Press (1979). - S. Sakai: C*-Algebras and W*-Algebras, Ergebnine der Mathematic und ihrer Grenzgebiete, Band 60, Springer-Verlag (1971). |
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| ADDITIONAL NOTES | Pre-requisite Qualifications: B.Sc. with Mathematics as a main area Follows from: MAT3210, MAT3211, MAT3219 |
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| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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