Math 597A Homework 2 Due October 6th, 2009
Exercise 1. Let E1 E2 . . . be a (strict) inductive sequence of barreled
topological vector spaces (Ei is a closed subspace of Ei+1 for each i). Show
that their inductive limit is also barreled.
Solution. Let B b
Math 597A Homework 3 Due October 27th, 2009
Exercise 1. Give (with proof) an example of a distribution on R and a
smooth, compactly supported function f such that f = 0 on Support()
but f = 0. Is it possible to give a similar example where f = 0 on a
Math 597A Homework 4 Due November 17th, 2009
Exercise 1. Let E, F be Banach spaces. Consider the canonical map (x, y )
x y of E F to the (projective) tensor product E F . What is the
derivative of this map at the point (x0 , y0 )?
Solution: All that matt