Quotient of subspace theorem
In mathematics, the quotient of subspace theorem is an important property of finite-dimensional normed spaces, discovered by Vitali Milman.
Let be an N-dimensional normed space. There exist subspaces Z ⊂ Y ⊂ X such that the following holds:
is uniformly isomorphic to Euclidean. That is, there exists a positive quadratic form Q on E, such that
with K > 1 a universal constant.
The statement is relative easy to prove by induction on the dimension of Z with a K that depends only on N; the point of the theorem is that K is independent of N.
In fact, the constant c can be made arbitrarily close to 1, at the expense of the
constant K becoming large. The original proof allowed
