Sizzling London and...Banach Spaces.

It's been sizzling in London...so here's some essential equipment. That's water...real H2O.

I'd appreciate it if someone could tell me what Banach algebra/spaces are...I mean, I know that Hilbert spaces are a type of Banach space, but I really need some introductory text on this and how they relate to Lie algebra (groups).