Ok, so I'm pretty much finished with my PhD and have started to look for postdoc positions. So far I've looked at mathjobs.org and EIMS and will contact people in my field (harmonic analysis and operator theory) and ask them to inform me if any kind...

I've seen the result all over the place, but no proof: The Lp-norm of a function f approaches the L-infty norm of f as p approaches infinity. Any illuminating clues? EDIT: We assume f is in L^p and L^infty, so that it's in L^q for all q > p.

Two question: 1. Let B(H,K) denote the space of bounded linear operators H --> K. Show B(H,K) is complete under the operator norm ||T|| = sup{ ||Th|| : h in H and ||h||≤1 }. I seem to really struggle with this operator norm guy. Obviously I want to...

Hi folks. Long time lurker here, and today I have a question. What sort of graduate schools would fit as "safety schools" for me when applying to graduate school? I'm currently an undergraduate in a school usually ranked in the top 25 so far as math...

Two posts in one day, sorry. Is the image of a compact linear operator (say, from H to K) necessarily open or closed? My instinct is that neither of these is necessarily true, but I'm having a tough time thinking of any counterexamples... Any...