MA 844 Topics in Analysis II (Aut 2011)
- Lectures: Mon 9:30 to 10:25 am, Tue
10:35 to 11:30 am, Thu 11.35 am to 12:30 pm in Room 114
Informations about the course:
- Content:
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Basic theory of C*-algebras and von Neumann algebras: positive
elements, Gelfand theory, continuous functional calculus, weak topologies, Predual, double commutant theorem, Kaplansky density theorem, ideals, GNS construction, representation
theorem of W*-algebras, second dual of C*-algebras, Factors.
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Text/References:
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1. W. Arveson: An Invitation to C*-algebras, Springer
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2. J. B. Conway: A course in Operator Theory, American Mathematical
Society
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3. K. Davidson: C*-algebras by Examples, American Mathematical
Society
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4. R. V. Kadison, J. R. Ringrose: Fundamental of Theory of Operator
Algebras-I and II, Academic Press.
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5. S. Sakai: C*-algebras and W*-algebras, Springer
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6. M. Takesaki: Theory of Operator Algebras, Springer
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Topics of student's talks (Fri 2-3:30 pm in Room 114):
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1. Spectrum is nonempty closed and bounded- G. Gorai ([8])
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2. Banach-Alaoglu theorem- G. Nair ([8])
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3. Dilation theory- S. Goyal, M.M. Radhika ([10],[11],[12],[14])
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4. Inner functions and Beurling's theorem- Anbu ([2],[12],[14])
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5. Canonial commutation relations (CCR)- G. Mallick ([7])
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6. Uniqueness of CCR- Sajith ([7],[15])
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7. Cuntz algebras- P. Bag ([3],[9])
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8. Factors- S. Poddar, H. Trivedi ([2],[4],[5],[6],[13])
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Additional references for talks: pdf
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As assignments students can take up some of the exercises given in books
listed under references.