I wanted to know are there any problems in Functional Analysis (FA) that can possibly be successfully tackled by someone like me who does not have any expertise in this area but is only familiar with a few basic topics that you would find in most undergraduate level courses?


I wanted to mention that I did look around the web before posting here. There doesn't seem to be much left that an undergrad can do in this area (or almost any other area), but I have seen sometimes papers by other researchers who in the end of their papers mention how their work can be used to do something (usually these are concrete applications or suggestions to work on specific examples), but the author didn't find the time or hadn't the resources to carry out the work and it's left to the interested reader. I wanted someone to help me find these kind of problems that would be easy to work on if I give it some time. 


My goal is to write a research paper and get it published in a suitable journal. I'm out of school at the moment and would like to get admission into a good PhD program. It is very hard for someone like me to get the attention of a professor to take me as a doctoral student without having proven first that I am motivated to and can do the work in FA.


Thank you for your time and help.



What are some problems for research in functional analysis that can possibly be solved by someone with basic knowledge of the subject?
Since your aim is to show your abilities and get the attention of a professor that would take you in a PhD program, the best and most natural thing would be, getting the problems from the professors themselves. Read their papers, find their open problems that you may like, and then write to them (with discretion) for clarifications or for suggestions of "easy cases" to start with. After all, this is how great Sofja Kovalevski got the attention of Weierstrass: solving his test problems in a week. Good luck!


