Course No
M452
Credit
4
Approval
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.