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राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान
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  2. MA604 - Analysis II

MA604 - Analysis II

By admin_sms on Thu, 12/03/2015 - 21:42
Course No
MA604
Credit
8
Approval
2018
PG-Core
Syllabus
Banach spaces: Review of Banach spaces, Hahn-Banach Theorem and its applications, Baire Category theorem and its applications like Closed graph theorem, Open mapping theorem.
Topological Vector spaces: Weak and weak* topologies, locally convex topological vector spaces. 
Hilbert spaces: Review of Hilbert spaces and operator Theory, Compact operators, Schauder's theorem on the spectral theory of compact operators.
Banach algebras: Elementary properties,  Resolvent and spectrum, Spectral radius formula,  Ideals and homomorphisms, Gelfand transforms, Gelfand theorem for commutative Banach algebras.
Reference Books
  1. D. S. Bridges, Foundations of Real and Abstract Analysis, GTM series, Springer Verlag 1997.
  2. G. B. Foland, Real Analysis: Modern Techniques and Their Applications (2nd ed.), Wiley-Interscience/John Wiley Sons, Inc., 1999.
  3. G. K. Pederson, Analysis NOW, GTM series, Springer-Verlag, 1991. 
  4. W. Rudin, Real and Complex Analysis, TMH Edition, Second Edition, New-York, 1962.
  5. W. Rudin, Functional Analysis, TMH Edition, 1974.
  6. K. Yosida, Functional Analysis, Springer-Verlag 1968.

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