Mathematics
Published on Mathematics (https://maths.iisuniv.ac.in)

Home > FUNCTIONAL ANALYSIS- I (Compulsory Paper)

FUNCTIONAL ANALYSIS- I (Compulsory Paper) [1]

Paper Code: 
MAT 321
Credits: 
5
Max. Marks: 
100.00
Unit I: 
I
15.00
Normed linear spaces. Quotient space of normed linear spaces and its completeness. Banach spaces and examples. Bounded and continuous linear transformations. 
 
Unit II: 
II
15.00
Normed linear space of bounded linear transformations. Equivalent norms. Basic properties of finite dimensional normed linear spaces and compactness. Reisz Lemma. 
 
Unit III: 
III
15.00
Multilinear mapping. Open mapping theorem. Closed graph theorem. Uniform boundness theorem. Continuous linear functionals. Hahn-Banach theorem and its consequences. 
 
Unit IV: 
IV
15.00
Hilbert space and its properties. Orthogonality and Functionals in Hilbert Spaces. Phythagorean theorem, Projection theorem, Orthonormal sets.
 
Unit V: 
V
15.00
Bessel’s inequality, Complete orthonormal sets, Parseval’s identity, Structure of a Hilbert space, Riesz representation theorem.
 
Essential Readings: 
  1. G.F.Simmons: Topology and Modern Analysis, McGraw Hill (1963) 
  2. G.Bachman and Narici : Functional Analysis, Academic Press 1964 
  3. A.E.Taylor : Introduction to Functional analysis, John Wiley and sons (1958) 
  4. A.L.Brown and Page : Elements of Functional Analysis, Van-Nastrand Reinehold Com 
  5. B.V. Limaye: Functional Analysis, New age international. 
  6. Erwin Kreyszig, Introductory functional analysis with application, Willey.
  7. Dileep S. Chauhan, Functional Analysis and calculus in Banach space, JPH. 
 
Academic Year: 
2015-2016 [2]

Footer Menu

  • Univ Home
  • Home
  • Contact Us
  • About Us
  • Site Map
  • Feedback
  • Site Login

Follow Mathematics on:

Facebook Twitter YouTube

IIS (Deemed to be University)

Gurukul Marg, SFS, Mansarovar, Jaipur 302020, (Raj.) India Phone:- +91-141-2400160-61, 2397906-07, Fax: 2395494, 2781158


Source URL: https://maths.iisuniv.ac.in/courses/subjects/functional-analysis-i-compulsory-paper-4

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/functional-analysis-i-compulsory-paper-4
[2] https://maths.iisuniv.ac.in/academic-year/2015-2016