Sentence examples for null sequence from inspiring English sources

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence.

It is shown that every weakly compact subset of a Banach space is contained in the closed convex hull of a weakly null sequence if and only if the Banach space has the Schur property.

Suppose that (Fn n=0∞ is a sequence of regular families of finite subsets of N such that F0 contains all singletons, and (θn)n=1∞ is a nonincreasing null sequence in (0,1).

We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in (∑Lpi ℓ2, where pi↓1, so that for all ε>0 and 1<q⩽2, every subsequence of (fi) admits a block basis (1+ε -equivalent to the Haar basis for Lq.

Therefore, { b n } is a null sequence.

so, also is a null sequence as.

for any and any weakly null sequence in.

Assume that is a weakly null sequence in and.

if { x n − x } n is a multi-null sequence.

if ( x n − x ) is a multi-null sequence.

Assume that ({x_{n}}) is a weak∗-null sequence, where by (w^) topology we mean the (sigma ell_{1},c_{0})) topology.