Measure, Integration & Real Analysis · Problem 6C.8

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · ell1-l1-norm-banach

Problem

Show that

\ell^1

with the norm defined by

\|(a_1, a_2, \ldots)\|_1 = \sum_{k=1}^\infty |a_k|

is a Banach space.