Conversation started May 4, 2012 at 12:07.
Matt N.
Matt N.
May 4, 2012 12:07
What does "complemented by a projection of norm 1" mean?
J. M.
J. M.
Well put, Ilya.
Ilya
Ilya
@JM was an obvious argument of mine. Even a trivial one
N3buchadnezzar
N3buchadnezzar
I tend to think that really good food tend to taste plain, and un interesting. Although salad seems to be an hilarious food to digest.
t.b.
t.b.
@MattN there's a norm one projection onto the subspace.
Matt N.
Matt N.
@tb So the subspace is the image of the projection. Ok, thanks.
t.b.
t.b.
May 4, 2012 12:14
@MattN yes, a subspace is said to be complemented if it is the image of a continuous projection. People say $K$-complemented if there's a projection of norm $\leq K$.
Matt N.
Matt N.
@tb What's wrong with for example $\ell^2$ with any one-dimensional subspace?
t.b.
t.b.
@MattN the question is whether it works in an arbitrary Banach space. Hahn-Banach only gives you a projection of norm $n$ or $\sqrt{n}$ if you're a bit more clever but you can't do much better in general.
 
Conversation ended May 4, 2012 at 12:15.