Definition talk:Compact Linear Transformation

I'm looking at all this work on Hilbert spaces, and seeing a lot of language in common with both linear algebra and topology. There's obvious contextual overlap. How easy would it be to exploit the parallelism, maybe be (a) establishing that a Hilbert space is a particular type of vector space(?) and therefore obeys various stuff which all vector spaces obeys, and (b) whichever aspects of it are also consistent with it being treated as a topological space 9? I haven't a clue what I'm talking about), and therefore etc. --prime mover 17:40, 23 February 2012 (EST)