Principles: Uniform Boundedness

So last week we talked about the Baire Category Theorem, and this important tool will give us three equivalent theorems about the qualitative properties of operators on Banach spaces. Today we will begin with the first theorem, uniform boundedness. The proof of this...

Principles: Baire’s Lemma

So today I am starting a new series on the Principles of Functional Analysis to give you all an appreciation for the power that these simple truths hold. We will start today with Baire’s Lemma , which will require some definitions, hopefully, all familiar. (If...

A Year in Hiatus!

This year has been rather crazy for me and so haven’t had much time to blog. The reason being that I completed my honours year in Australia in 6 months instead of the full year (they thought it was impossible, but I did it!) which required a lot of time and...

Logic and direct proofs

In a direct proof we deal with If P then Q types of statements, more formally known as conditionals. An example of a conditional, is “If n is an odd integer, then n^2 is odd.” However, it might not be worded like this, it could have been, “The square...

Intoduction

I’m Anthony Salib, a student at Monash University Australia and studying physics and maths. This blog is going to highlight somethings that are find interesting, or useful!