# zbMATH — the first resource for mathematics

On a new class of sequences related to the space $$\ell^p$$. (English) Zbl 1005.46002
The authors define a new sequence space, which is a generalization of a space due to Sargent, and show that it is a Banach space in which the coordinate maps are continuous; furthermore it is symmetric, normal and lies between the spaces $$\ell^p$$ and $$\ell^\infty$$. They also give conditions implying that their new space should be identical with $$\ell^p$$ or $$\ell^\infty$$, respectively.

##### MSC:
 46A45 Sequence spaces (including Köthe sequence spaces) 40A05 Convergence and divergence of series and sequences
##### Keywords:
sequence space; Banach space