# User:Caliburn

b. 04/03/2001 from Kent. Call me George rather than Caliburn.

BSc Maths from Warwick (2019-2022). Part III Maths (2022-).

Interested in analysis and probability.

## Functional Analysis to do

• Integration on Banach spaces - I will be doing this with the Bochner integral rather than Riemann integral. Riemann integral will come later if necessary, but ATM we're just going to be integrating continuous functions on compact intervals where the two integrals are equivalent. Analogous to Lebesgue vs Riemann.
• Dual space of $L^p$ and $\map C K$
• Weak and Weak-$\ast$ topology to include Goldstine's theorem, results about the weak and weak-$\ast$ topologies on unit balls (NVS reflexive iff unit ball weakly compact for example)
• The very basics of Banach algebras, then Holomorphic Functional Calculus (needs integration theory quite extensively)
• $C_0$ semigroups of operators, to include Hille-Yosida, Lumer-Phillips (needs integration theory extensively again)