Revista de la
Unión Matemática Argentina
$p$-Dual frames and $p$-Riesz sequences in quasinormed spaces
José Alfonso López Nicolás
Volume 61, no. 2 (2020), pp. 291–301

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The present contribution is aimed at obtaining new results in duality between $p$-dual frames and $p$-Riesz sequences in quasinormed spaces with a normalized Schauder basis. We obtain two results which show the relationship of duality between these concepts. We split a quasinormed space into a topological sum of two subspaces and use the Schauder basis to establish a relationship between the $p$-dual frames of one of these subspaces and the $p$-Riesz sequences of the dual of the other one. In fact, the main results are stated in a lightly more general context.