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राष्ट्रीय विज्ञान शिक्षा एवंअनुसंधान संस्थान
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  2. M452 - Advanced Functional Analysis

M452 - Advanced Functional Analysis

By admin_sms on Wed, 16/07/2014 - 15:55
Course No
M452
Credit
4
Approval
2014
UG-Elective
Syllabus
Definition and examples of topological vector spaces (TVS) and locally convex spaces (LCS); Linear operators; Hahn-Banach Theorems for TVS/ LCS (analytic and geometric forms); Uniform boundedness principle; Open mapping theorem; Closed graph thoerem; Weak and weak* vector topologies; Bipolar theorem; dual of LCS spaces; Krein-Milman theorem for TVS; Krien-Smulyan theorem for Banach spaces; Inductive and projective limit of LCS.
Reference Books

W. Rudin, “Functional Analysis”, Tata McGraw-Hill, 2007.A. P. Robertson, W. Robertson, “Topological Vector Spaces”, Cambridge Tracts in Mathematics 53, Cambridge University Press, 1980.J. B. Conway, “A Course in Functional Analysis”, Graduates Texts in Mathematics 96, Springer, 2006.

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