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राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान
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  2. M557 - Operator Algebras

M557 - Operator Algebras

By admin_sms on Thu, 17/07/2014 - 14:35
Course No
M557
Credit
4
Approval
2014
UG-Elective
Syllabus
Banach algebras/C*–algebras: Definition and examples; Spectrum of a Banach algebra; Gelfand transform; Gelfand-Naimark theorem for commutative Banach algebras/ C*-algebras; Functional calculus for C*-algebras; Positive cone in a C*-algebra; Existance of an approximate identity in a C*- algebra; Ideals and Quotients of a C*-algebra; Positive linear functionals on a C*-algebra; GNS construction. Locally convex topologies on the algebras of bounded operators on a Hilbert space, von-Neumann’s bi-commutant theorem; Kaplansky’s density theorem. Ruan’s characterization of Operator Spaces (if time permites).
Reference Books
  1. R. V. Kadison, J. R. Ringrose, “Fundamentals of the Theory of Operator Algebras Vol. I”, Graduate Studies in Mathematics 15, American Mathematical Society, 1997.
  2. G. K. Pedersen, “C*–algebras and their Automorphism Groups”, London Mathematical Society Monographs 14, Academic Press, 1979.
  3. V. S. Sunder, “An Invitation to von Neumann Algebras”, Universitext, Springer-Verlag, 1987.
  4. M. Takesaki, “Theory of Operator Algebras Vol. I”, Springer-Verlag, 2002.

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