I am a masters 1st year student and my functional analysis course ended 1 week ago. The instructor followed Irwin Krieszig's Book " Introductory Functional Analysis with Applications" for teaching and although he didn't gave any assignments or exercise problems, I solved problems from exercises given in Krieszig's Book. I was able to understand the concepts given in the book clearly and then do exercises of Krieszig without much difficulty. But I noticed that the problems of the book are much easier for a masters student but as I was busy in some extra - curricular activities also , so I didn't tried other problems or asked for reference books or materials here.
But Now I think that I must solve good number of Challenging problems in Functional Analysis as I will apply for phd in pure mathematics soon and I got my December break time to it.
So, Can you please tell any book in functional analysis course whose exercises are challenging as compared to Krieszig's / any assignments which any professor of a university gave which are available on web?
Also, I am adding my course syllabus in the following images so that you come to know exactly which topics should be available( I absolutely no problem If more topics are covered). All these topics were covered which are given in the images and none except them were covered.
Edit: I am good in measure theory , so if any functional analysis book you are recommending assumes knowledge of measure theory then I am fine with it.
Looking for your help.