Abstract :

The uniform boundedness principle, the open mapping theorem and the closed graph theorem are considered as three grand theorems in functional analysis. These theorems have a lot of applications in different fields. In this talk, we will give an elementary proof of the uniform boundedness principle using basic real analysis tools and will establish the equivalence of these theorems in the Hilbert space setting. This talk will be based on Prof. S Kesavan's article "A Note on the Grand Theorems of Functional Analysis", which appeared in Mathematical Newsletter (Volume 27, No. 3, December - March 2017). This talk will be accessible to all.