Talk:Finite Rank Operators Dense in Compact Linear Transformations

Further to my note about Hilbert Spaces being treated as topological spaces, do we need a comment about what "everywhere dense" means in a Hilbert space? --prime mover 01:54, 24 February 2012 (EST)

Probably that is a good idea. What do you think of my amendment? --Lord_Farin 04:01, 24 February 2012 (EST)

That would work. Still to do:

a) use this as a definition for "everywhere dense" in this context;

b) establish that this def is consistent with E.D. in the context of a topological space: Hilbert space as a generalisation of the Euclidean space which of course is a topology, etc. etc. Messy old business. --prime mover 09:06, 24 February 2012 (EST)

Part b) boils down to proving the equivalence of the limit points definitions (which stands as a stub atm); this is merely an instantiation of the sequence definition of limit point (true, true; it presupposes that a norm induces a metric, which then induces a topology). --Lord_Farin 09:31, 24 February 2012 (EST)