Measure, Integration & Real Analysis · Problem 6C.7

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · ell1-sup-norm-not-banach

Problem

Show that

\ell^1

with the norm defined by

\|(a_1, a_2, \ldots)\|_\infty = \sup_{k \in \mathbf{Z}^+} |a_k|

is not a Banach space.