I am wondering if there exist examples of Banach (or Frechet) sequence spaces in which the set of all finite support sequences are NOT dense?
2026-04-02 08:54:44.1775120084
An example of a separable Banach sequence space in which the finite support sequences are not dense?
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Probably the simplest example is $c$, the space of convergent sequences. The closure of the finitely supported sequences is, of course, $c_0$, the space of null sequences.