Recent content by ScroogeMcDuck

Suppose for each given natural number n I have a convergent sequence (y_i^{(n)}) (in a Banach space) which has a limit I'll call y_n and suppose the sequence (y_n) converges to y. Can I construct a sequence using elements (so not the limits themselves) of the sequences (y_i^{(n)}) which...

Sorry for the rather vague title! Homework Statement Given: Two Banach spaces A and B, and a linear map T: A\rightarrow B The sequences (x^n_i) in A. For each fixed n, (x^n_i) \rightarrow 0 for i \rightarrow \infty. The sequences (Tx^n_i) in B. For each fixed n, (Tx^n_i) \rightarrow y_n...