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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

6 votes
3 answers
2k views

reflexive banach space

I want to ask this non-expert question: What does it mean geometrically for a Banach space to be reflexive? Well, we could say a Banach space is reflexive iff unit ball is weakly compact. Or some ot …
alpx's user avatar
  • 351
3 votes
0 answers
148 views

Average nastiness of a Newton polytope

Given a Newton polytope $P$ inside the $d$-scaled simplex ( i.e $\alpha \in P \implies | \alpha |=d $ ), then we define the following quantity: $$ P(x)= \left( \sum_{\alpha \in P} \binom{d}{\alpha …
alpx's user avatar
  • 351
4 votes

What is the interface between functional analysis and algebraic geometry?

I do not know if this is what you are looking for but I heard people speaking of Banach Algebraic Geometry. I can also note the fascinating work of Semyon Alesker (using algebra-geometric tools on say …
alpx's user avatar
  • 351